See typed list
of tables in
side this cover
1916, 1930, 1951, 1934, and 1956 editions of
(tables in back of book)
(1916)
fable So. litle
% Traverse table, degrees
Conversion of departure into differ-
531
621
634
755
772
817
5
5B
42
44
45
not in these editions - refer to
1958 edition, Table 4, pace 106)
Meridional parts
Distance of an object by tso bear
ings, degrees
tables
(not in these editions - refer to
1988 edition, Table l? JL j^ i se_140>
Logarittes of numbers
Logarithms of trigonometric func
tions, degrees
Logarithmic and natural haversines
i
No. 9
American Practical Navigator
An Epitome of Navigation and
Nautical Astronomy
ORIGINALLY BY
NATHANIEL BOWDITCH, LL. D.
PUBLISHED BY THE
UNITED STATES HYDROGRAPHIC OFFICE
UNDER THE AUTHORITY OF
THE SECRETARY OF THE NAVY
WASHINGTON
GOVERNMENT PRINTING OFFICE
1916
y /
/
Mtton.
STATUTES OF AUTHOKIZATION.
There shall be a Hydrographic Office attached to the Bur.eau of Navigation in
the Navy Department, for the improvement of the means for navigating safely
the vessels of the Navy and of the mercantile marine, by providing, under the
authority of the Secretary of the Navy, accurate and cheap nautical charts, sailing
directions, navigators, and manuals of instructions for the use of all vessels of the
United States, and for the benefit and use of navigators generally. (R. S. 431.)
The Secretary of the Navy is authorized to cause to be prepared, at the Hydro-
graphic Office attached to the Bureau of Navigation in the Navy Department,
maps, charts, and nautical books relating to and required in navigation, and to
publish and furnish them to navigators at the cost of printing and paper, and to
purchase the plates and copyrights of such existing maps, charts, navigators, sail
ing directions, and instructions, as he may consider necessary, and when he may
deem it expedient to do so, and under such regulations and instructions as he may
prescribe. (R. S. 432.)
2
r
TEXT AND APPENDICES.
.300861
NOTE ON REPRINT OF 1916. This reprint is the same as the 1914 edition, except
that the examples worked out in the text have been brought up to date to accord with
the form of the American Nautical Almanac as now published.
CONTENTS OF F^RT I.
Page.
Abbreviations
Chapter I. Definitions relating to Navigation 9
II. Instruments and Accessories in Navigation 11
III. The Compass Error 36
IV. Piloting 56
V. The Sailings 72
VI. Dead Reckoning 84
VII. Definitions relating to Nautical Astronomy 87
VIII. Instruments employed in Nautical Astronomy 91
IX. Time and the Nautical Almanac 102
X. Correction of Observed Altitudes 115
XI. The Chronometer Error 121
XII. Latitude 126
XIII. Longitude 140
XIV. Azimuth 144
XV. The Sumner Line 150
XVI. The Practice of Navigation at Sea 169
XVII. Marine Surveying 189
XVIII. Winds 206
XIX. Cyclonic Storms 212
XX. Tides 225
XXI. Ocean Currents 232
XXII. Ice and its Movements in the North Atlantic Ocean 238
Appendix I. Extracts from the American Ephemeris and Nautical Almanac for the year 1916
which have reference to examples for that year given in this work 248
II. A collection of Forms for working Dead Reckoning and various Astronomical Sights,
with notes explaining their application under all circumstances 254
III. Explanation of certain Rules and Principles of Mathematics of use in the Solution
of Problems in Navigation 266
IV. Maritime Positions and Tidal Data ; 278
Index.. 358
ABBREVIATIONS USED IN THIS WORK.
Alt. (or ft) Altitude.
a. m Ante meridian.
Amp Amplitude.
App Apparent.
App. t Apparent time.
Ast Astronomical.
Ast. t Astronomical time.
Aug Augmentation.
Az. (orZ) Azimuth.
C Course.
C. C Chronometer correction.
C W Chronometer minus watch.
Chro. t Chronometer time.
Co. L Co. latitude.
Col Column.
Corr Correction.
Cos Cosine.
Cosec Cosecant.
Cot Cotangent.
d (or Dec.) Declination.
D (or D.Lo) Difference longitude.
Dep Departure.
Dev Deviation.
Diff Difference.
Dist Distance.
DL Difference latitude.
D. R Dead reckoning.
E., Ely East, easterly.
Elap. t Elapsed time.
Eq. t Equation of time.
F Longitude factor.
/ Latitude factor.
G. (or Gr.) Greenwich.
G. A. T Greenwich apparent time.
G. M. T Greenwich mean time.
G. S. T Greenwich sidereal time.
ft Altitude.
H Meridian altitude.
H. A. (or t) Hour angle.
Hav Haversine.
H. D Hourly difference.
H. P. (or Hor. par.). .Horizontal parallax.
Hr-s Hour-s.
H. W High water.
I. C Index correction.
L. (or Lat.) Latitude.
L. A. T Local apparent time.
L. M. T Local mean time.
L. S. T Local sidereal time.
Lo. (or Long.) Longitude.
Log Logarithm.
Lun. Int Lunitidal interval.
L. W Low water.
A Longitude.
m Meridional difference.
Merid Meridian or noon.
Mag Magnetic.
M. D Minute s difference.
Mid Middle.
Mid. L Middle latitude.
M. T Meantime.
nat Natural.
N., Nly North, northerly.
N. A. (orNaut. Aim.) Nautical Almanac.
Np Neap .
Obs Observation.
p (or P. D.) Polar distance.
p. c Per compass.
JP. D. (or p) Polar distance.
P. L. (or Prop. Log.). Proportional logarithm.
p. m Post meridian.
p, & r Parallax and refraction.
rar Parallax.
R. A Right ascension.
R. A. M. S Right ascension mean sun.
Red Reduction.
Ref Refraction.
S., Sly South, southerly.
S. D Semidiameter.
Sec Secant.
Sid Sidereal.
Sin Sine.
Spg Spring.
t Hour angle.
T Time.
Tab Table.
Tan Tangent.
Tr. (or Trans. ) Transit.
Var Variation.
Vert Vertex or vertical.
W., Wly West, westerly.
W. T Watch time.
z Zenith distance.
Z Azimuth.
6 Auxiliary angle.
X Difference longitude in time.
SYMBOLS.
The Sun.
The Moon.
* _ A Star or Planet.
"Q (C Alt. upper limb.
L Q ([_ Alt. lower limb.
(J) |3 Azimuthal angle.
A a ..Alpha.
/? ..Beta.
F Y ..Gamma.
Ad.. Delta.
E e . .Epsilon.
Z C -.Zeta.
Hr) ..Eta.
8 d ..Theta.
Iota.
Kappa.
Lambda.
u.
GREEK LETTERS.
f.
I
K K
A X
M it
Degrees.
Minutes of Arc.
Seconds of Arc.
Hours.
Minutes of Time.
Seconds of Time.
N v Nu.
s e xi.
o Omicron.
n 7i Pi.
, P p Rho.
1 a (r)... Sigma.
T T Tau.
T y Upsilon.
<j> Phi.
X x Chi.
</> Psi.
Q a> Omega .
CHAPTER I.
DEFINITIONS KELATING TO NAVIGATION,
1. That science, generally termed Navigation, which affords the knowledge
necessary to conduct a ship from point to point upon the earth, enabling the mariner
to determine, with a sufficient degree of accuracy, the position of his vessel at any
tune, is properly divided into two branches : Navigation and Nautical Astronomy.
2. Navigation, in its limited sense, is that branch which treats of the determina
tion of the position of the ship by reference to the earth, or to objects thereon. It
comprises (a) Piloting, in which the position is ascertained from visible objects
upon the earth, or from soundings of the depth of the sea, and (b) Dead Reckoning,
in which the position at any moment is deduced from the direction and amount of
a vessel s progress from a known point of departure.
3. Nautical Astronomy is that branch of the science which treats of the deter
mination of the vessel s place by the aid of celestial objects the sun, moon, planets,
or stars.
4. Navigation and Nautical Astronomy have been respectively termed Geo-
Navigation and Celo- Navigation, to indicate the processes upon which they depend.
5. As the method of piloting can not be employed excepting near land or in
moderate depths of water, the navigator at sea
must fix his position either by dead reckoning or by
observation of celestial objects; the latter method is
more exact, but as it is not always available, the
former must often be depended upon.
6. THE EARTH. The Earth is an oblate
spheroid, being a nearly spherical, body slightly
flattened at the poles; its longer or equatorial
axis measures about 7,927 statute miles, and its E
shorter axis, around which it rotates, about 7,900
statute miles.
The Earth (assumed for purposes of illustra
tion to be a sphere) is represented in figure 1.
The Axis of Rotation, usually spoken of simply
as the Axis, is PP .
The Poles are the points, P and P , in which
the axis intersects the surface, and are designated,
respectively, as the North Pole and the South Pole.
The Equator is the great circle EQMW, formed by the intersection with the
earth s surface of a plane perpendicular to the axis ; the equator is equidistant from
the poles, every point upon it being^90 from each pole.
Meridians are the great circles rQP , PMP , PM P , formed by the intersection
with the earth s surface of planes secondary to the equator (that is, passing through
its poles and therefore perpendicular to its plane).
Parallels of Latitude are small circles NTn, N n T , formed by the intersection
with the earth s surface of planes passed parallel to the equator.
The Latitude of a place on the surface of the earth is the arc of the meridian
intercepted between the equator and that place. Latitude is reckoned North and
South, from the equator as an origin, through 90 to the poles; thus, the latitude
of the point T is MT, north, and of the point T , MT, north. The Difference of
Latitude between any two places is the arc of a meridian intercepted between their
parallels of latitude, and is called North or South, according to direction; tnus, the
difference of latitude between T and T is Tn f or T n, north from T or south from T .
The Longitude of a place on the surface of the earth is the arc of the equator inter
cepted between its meridian and that of some place from which the longitude is
9
FIG. l.
10 ... fc .. DEFINITION RELATING TO NAVIGATION.
reckoned. Longitude is measured East or West through 180 from the meridian of
a designated- place, such meridian being termed the Prime Meridian; the prime
meridian used by most nations, including the United States, is that of Greenwich,
England. If, in the figure, the prime meridian be PGQP , then the longitude of the
point T is QM, east, and of T , QM , east. The Difference of Longitude between any
two places is the arc of the equator intercepted between their meridians, and is called
East or West, according to direction ; thus, the difference of longitude between T and
T is MM , east from M or west from M . The Departure is the linear distance,
measured on a parallel of latitude, between two meridians; unlike the various quanti
ties previously defined, departure is reckoned in miles; the departure between two
meridians varies with the parallel of latitude upon which it is measured; thus, the
departure between the meridians of T and T is the number of miles corresponding
to the distance Tn in the latitude of T, or to n T in the latitude of T .
The curved line which joins any two places on the earth s surface, cutting all the
meridians at the same angle, is called the Rhumb Line, Loxodromic Curve, or Equian
gular Spiral. In the figure this line is represented by TYT . The constant angle
which this line makes with the meridians is called the Course; and the length of the
line between any two places is called the Distance between those places;
The unit of linear measure employed by navigators is the Nautical or Sea Mile,
or Knot. This unit is defined in the United States of America as being 6,080.27
feet in length and equal to one-sixtieth part of a degree of a great circle ot a sphere
whose surface is equal in area to the area of the surface of the earth.
The nautical mile is not exactly the same in all countries, but, from the navi
gator s standpoint, the various lengths adopted do not differ materially.
Since, upon the ocean, latitude has been capable of easier and more accurate
determination than longitude, it might naturally be expected that there exists an
intimate fixed relation between the nautical mile and the minute of latitude (or the
length of that portion of a meridian which subtends at the earth s center the angular
measure of one minute); but on account of the fact that the earth is not a perfect
sphere, a fixed relation does not exist, and the arc of a meridian that subtends an
angle of 1 at the center of the earth varies slightly in length from the Equator to
the poles, being 6,045.95 feet at the Equator and 6,107.85 feet at the poles. Its
average length is 1,852.201 meters, or 6,076.82 feet. Accordingly in France,
Germany, and Austria the nautical mile is 1,852 meters, 2,025.41 yards, or 6,076.23
feet.
For purposes of navigation the nautical mile is assumed to be equal to a minute
of latitude in all parts of the world; and, hence, when a vessel changes her position
to the north or south by 1 nautical mile, it may always be considered that the latitude
has changed 1 . Owing to the fact that the meridians converge toward the poles,
the difference of longitude produced by a change of position ol 1 mile to the east
or west will vary with the latitude ; thus, a departure of 1 mile will equal a difference of
longitude of 1 at the Equator, but of more than 1 at any higher latitude, being in
fact equal to I .l of longitude in latitude 30 and to 2 of longitude in latitude 60.
In England the nautical mile, corresponding to the Admiralty knot, is regarded
as having a length of 6,080 feet.
The statute mile of 5,280 feet, which is employed in land measurements, is
commonly used in navigating river and lake vessels. This is notably the case on the
Great Lakes of America, but with the recognition of the advantages to be gamed by
the nractice of nautical astronomy in the navigation of these vessels, the use of the
nautical mile is extending.
The Great Circle Track or Course between any two places is the route between
those places along the circumference of the great circle which joins them. In the
figure this line is represented by T/T . From the properties of a great circle (which is a
circle upon the earth s surface formed by the intersection of a plane passed through
its center) the distance between two points measured on a great circle track is shorter
than the distance upon any other line which joins them. Except when the two
points are on the same meridian or when both lie upon the equator, the great circle
track will always differ from the rhumb line, and the great circle track wul intersect
each intervening meridian at a different angle.
CHAPTER II.
INSTRUMENTS AND ACCESSORIES IN NAVIGATION,
DIVIDERS OB COMPASSES.
7. This instrument consists of two legs movable about a joint, so that the
points at the extremities of the legs may be set at any required distance from each
other. It is used to take and transfer distances and to describe arcs and circles.
When used for the former purpose it is termed dividers, and the extremities of both
legs are metal points; when used for describing arcs or circles, it is called a compass,
and one of the metal points is replaced by a pencil or pen.
PARALLEL RULERS.
8. Parallel rulers are used for drawing lines parallel to each other in any direc
tion, and are particularly useful in transferring the rhumb-line on the chart to the
nearest compass-rose to ascertain the course, or to lay off bearings and courses.
PROTRACTOR.
9. This is an instrument used for the measurement of angles upon paper;
there is a wide variation in the material, size, and shape in which it may be made.
(For a description of the Three Armed Protractor, see art. 428, Chap. XVII.)
THE CHIP LOG.
10. This instrument, for measuring the rate of sailing, consists of three parts;
viz, the log-chip, the log-line, and the log-glass. A light substance thrown from the
ship ceases to partake of the motion 01 the vessel as soon as it strikes the water,
and will be left behind on the surface; after a certain interval, if the distance of the
ship from this stationary object be measured, the approximate rate of sailing will
be given. The log-chip is the float, the log-line is the measure of the distance, and
the log-glass defines the interval of tune.
The log-chip is a thin wooden quadrant of about 5 inches radius, loaded with
lead on the circular edge sufficiently to make it float upright in the water. There
is a hole in each corner of the log-chip, and the log-line is knotted in the one at the
apex; at about 8 inches from the end there is seized a wooden socket; a piece of
line of proper length, being knotted in the other holes, has seized into its bight a
wooden peg to fit snugly into the socket before the log-chip is thrown; as soon as
the line is checked this peg pulls out, thus allowing the log-chip to be hauled in
with the least resistance.
The log-line is about 150 fathoms in length, one end made fast to the log-chip,
the other to a reel upon which it is wound. At a distance of from 15 to 20 fathoms
from the log-chip a permanent mark of red bunting about 6 inches long is placed
to allow sufficient stray line for the log-chip to clear the vessel s eddy or wake. The
rest of the fine is divided into lengths of 47 feet 3 inches called Jcnots, by pieces of
fish-fine thrust through the strands, with one, two, three, etc., knots, according to
the number from stray-fine mark; each knot is further subdivided into five equal
lengths of two-tenths of a knot each, marked by pieces of white rag.
The length of a knot depends upon the number of seconds which the log-glass
measures; the length of each knot must bear the same ratio to the nautical mile
(-gV of a degree of a great circle of the earth, or 6,080 feet) that the time of the glass
does to an hour.
11
12 INSTRUMENTS AND ACCESSORIES IN NAVIGATION.
In the United States Navy all log-lines are marked for log-glasses of 28 seconds,
for which the proportion is :
3600 : 6080 = 28 s : x,
x being the length of the knot.
Hence,
z = 47 ft .29, or47 ft 3 in .
The speed of the ship is estimated in knots and tenths of a knot.
The log-glass is a sand glass of the same shape and construction as the old hour
glass. Two glasses are used, one of 28 seconds and one of 14 seconds; the latter is
employed when the ship is going at a high rate of speed, the number of knots indi
cated on a line marked for a 28-second glass being doubled to obtain the true rate
of speed.
11. The log in all its parts should be frequently examined and adjusted; the
Eeg must be found to fit sufficiently tight to keep the log-chip upright; the log-
ne shrinks and stretches and should often be verified; the log-glass should be
compared with a watch. One end of the glass is stopped with a cork, by removing
which the sand may be dried or its quantity corrected.
12. A ground log consists of an ordinary log-line, with a lead attached instead
of a chip; in shoal water, where there are no well-defined objects available for fixing
the position of the vessel and the course and speed are influenced by a tidal or other
current, this log is sometimes used, its advantage being that the lead marks a sta
tionary point to which motion may be referred, whereas the chip would drift with
the stream. The speed, which is marked in the usual manner, is the speed over
the ground, and the trend of the line gives the course actually made good by the
vessel.
THE PATENT LOG.
13. This is a mechanical contrivance for registering the distance actually run
by a vessel through the water. There are various types of patent logs, but for the
most part they act upon the same principle, consisting of a registering device, a fly
or rotator, and a log or towline; the rotator is a small spino3e with a number of
blades extending radially in such manner as to form a spiral, and, when drawn through
the water in the direction of its axis, rotates about that axis after the manner of a
screw propeller; the rotator is towed from the vessel by means of a log or towline
from 30 to 100 fathoms in length, made fast at its apex, the line being of special
make, so that the turns of the rotator are transmitted through it to. the worm shaft
of the register, to which the inboard end of the line is attached; the registering
device is so constructed as to show upon a dial face the distance run, according to
the number of turns of its worm shaft due to the motion of the rotator; the register
is carried at some convenient point on the vessel s quarter; it is frequently found
expedient to rig it out upon a small boom, so that the rotator will be towed clear
of the wake.
14. Though not a perfect instrument, the patent log affords a means of deter
mining the vessel s speed through the water. It will usually be found that the
indications of the log are in error by a constant percentage, and the amount of this
error should be determined by careful experiment and applied to all readings.
Various causes may operate to produce inaccuracy of working in the patent
log, such as the bending of the blades of the rotator by accidental blows, fouling of
the rotator by seaweed or refuse from the ship, or mechanical wear of parts of the
register. The length of the towline has much to do with the working of the log,
and by varying the length the indications of the instrument may sometimes be
adjusted when the percentage of error is small; it is particularly important that the
line shall not be too short. The readings of the patent log can not be depended upon
for accuracy at low speeds, when the rotator does not tow horizontally, nor in a head
or a following sea, when the effect depends upon the wave motion as well as upon
the speed of the vessel.
15. Electrical registers for patent logs are in use, the distance recorded by the
mechanical register being communicated electrically to some point of the vessel
which is most convenient for the purposes of those charged with the navigation.
INSTRUMENTS AND ACCESSORIES IN NAVIGATION.
13
17 fathoms from the lead, same as at 7 fathoms.
20 fathoms from the lead, with 2 knots.
25 fathoms from the lead, with 1 knot.
30 fathoms from the lead, with 3 knots.
35 fathoms from the lead, with 1 knot.
40 fathoms from the lead, with 4 knots.
And so on.
16. A number of instruments based upon different physical principles have
been devised for recording the speed of a vessel through the water and have been
used with varying degrees of success. Of these the hydraulic speed indicator, known
as the Nicholson Ship Log, affords an instance.
17. The revolutions of the screw propeller afford in a steamer the most valuable
means of determining a vessel s speed through the water. The number of revolu
tions per knot must be carefully determined for the vessel by experiment under
varying conditions of speed, draft, and foulness of bottom.
THE LEAD.
18. This device, for ascertaining the depth of water, consists essentially of a
suitably marked line, having a lead attached to one of its ends. It is an invaluable
aid to the navigator in shallow water, particularly in thick or foggy weather, and is
often of service when the vessel is out of sight of land.
Two leads are used for soundings the Tiand-lead, weighing from 7 to 14 pounds,
with a line marked to about 25 fathoms, and the deep-sea lead, weighing from 30 to
100 pounds, the line being 100 fathoms or upward in length.
Lines are generally marked as follows :
2 fathoms from the lead, with 2 strips of leather.
3 fathoms from the lead, with 3 strips of leather.
5 fathoms from the lead, with a white rag.
7 fathoms from the lead, with a red rag.
10 fathoms from the lead, with leather having a
hole in it.
13 fathoms from the lead, same as at 3 fathoms.
15 fathoms from the lead, same as at 5 fathoms.
Fathoms which correspond with the depths marked are called marks; the inter
mediate fathoms are called deeps; the only fractions of a fathom used are a half
and a quarter.
A practice sometimes followed is to mark the hand-lead line in feet around the
critical depths of the vessel by which it is to be used.
Lead lines should be measured frequently while wet and the correctness of the
marking verified. The distance from the leadsman s hand to the water s edge should
be ascertained in order that proper allowance may be made therefor in taking
soundings at night.
19. The deep-sea lead may be armed by filling with tallow a hole hollowed out
in its lower end, by which means a sample of the bottom is brought up.
THE SOUNDING MACHINE.
20. This machine possesses advantages over the deep-sea lead, for which it is
a substitute, in that soundings may be obtained at great depths and with rapidity
and accuracy without stopping the ship. It consists essentially of a stand holding
a reel upon which is wound the sounding wire, and which is controlled by a suitable
brake. Crank handles are provided for reeling in the wire after the sounding has
been taken. Attached to the outer end of the wire is the lead, which has a cavity
at its lower end for the reception of the tallow for arming. Above the lead is a
cylindrical case containing the depth-registering mechanism; various devices are in
use for this purpose, all depending, however, upon the increasing pressure of the
water with increasing depths.
21. In the Lord Kelvin machine a slender glass tube is used, sealed at one end
and open at the other, and coated inside with a chemical substance which changes
color upon contact with sea water; this tube is placed, closed end up, in the metal
cylinder; as it sinks the water rises in the tube, the contained air being compressed
with a force dependent upon the depth. The limit of discoloration is marked by a
clearly defined line, and the depth of the sounoling corresponding to this line is read
off from a scale. Tubes that have been used in comparatively shallow water may
be used again where the water is known to be deeper.
22. A tube whose inner surface is ground has been substituted for the chemical-
coated lube, ground glass, when wet, showing clear. The advantage of these tubes
14
INSTRUMENTS AND ACCESSORIES IN NAVIGATION.
is that they may be used an indefinite number of times if thoroughly dried. To
facilitate drying, a rubber cap is fitted to the upper end, which, when removed,
admits of a circulation of the air through the tube.
23. As a substitute for the glass tubes a mechanical depth recorder contained in a
suitable case has been used. In this device the pressure of the water acts upon a
piston against the tension of a spring. A scale with an index pointer records the
depth reached. The index pointer must be set at zero before each sounding.
24. Since the action of the sounding machine, when glass tubes are used,
depends upon the compression of the air, the barometric pressure of the atmosphere
must be taken into account when accurate results are required. The correction
consists in increasing the indicated depth by a fractional amount according to the
following table :
Bar. reading.
Increase.
29.75
One-fortieth.
30.00
One-thirtieth.
30.50
One- twentieth.
30.75
One-fifteenth.
THE MARINER S COMPASS.
25. The Mariner s Compass is an instrument consisting either of a single
magnet, or, more usually, of a group of magnets, which, being attached to a graduated
circle pivoted at the center and allowed to swing freely in a horizontal plane, has a
tendency, when not affected by disturbing magnetic features within the ship, to lie
with its magnetic axis in the plane of the earth s magnetic meridian, thus affording a
means of determining the azimuth, or horizontal angular distance from that meridian,
of the ship s course and of all visible objects, terrestrial or celestial.
26. The circular card of the compass is divided on its periphery into 360,
frequently numbered from at North and South to 90 at East and West; also
into thirty-two divisions of 11J each, called points, the latter being further divided
into naif-points and quarter-points; still finer subdivisions, eighth-points, are some-
tunes used, though not indicated on the card. A system of numbering the degrees
from to 360, always increasing toward the right, is shown in figure 2. This
system is in use in the United States Navy and by the mariners of some foreign
nations, and its general adoption would carry with it certain undoubted advantages.
27. Boxing the Compass is the process of naming the points in their order, and is
one of the first things to be learned by the young mariner. The four principal points
are called cardinal points and are named North, South, East, and West; each differs
in direction from the adjacent one by 90, or 8 points. Midway between the cardinal
points, at an angular distance of 45, or 4 points, are the inter-cardinal points, named
according to their position Northeast, Southeast, etc. Midway between each
cardinal and inter-cardinal point, at an angular distance of 22, or 2 points, is a
point whose name is made up of a combination of that of the cardinal with that of
the inter-cardinal point: North-Northeast, East-Northeast, East-Southeast, etc. At
an angular distance of 1 point, or 11J, from each cardinal and inter-cardinal point
(and therefore midway between it and the 22-division last described), is a point
which bears the name of that cardinal or inter-cardinal point joined by the word by
to that of the cardinal point in the direction of which it lies : North by East, Northeast
by North, Northeast by East, etc.
INSTRUMENTS AND ACCESSORIES IN NAVIGATION.
15
In boxing by fractional points, it is evident that each division may be referred to
either of the whole points to which it is adjacent; for instance, NE. by N. N. and
NNE. E. would describe the same division. It is the custom in the United States
Navy to box from North and South toward East and West, excepting that divisions
adjacent to a cardinal or inter-cardinal point are always referred to that point; as
No. 1742
JUNE 1908
FIG. 2.
N. i E., N. by E. E., NNE. $ E., NE. N., etc. Some mariners, however, make it a
practice to box from each cardinal and inter-cardinal point toward a 22 J-point (NNE.,
ENE., etc.); as N. * E., N. by E. J E., NE. by N. * N., NE. i N., etc.
The names of the whole points, together with fractional points (according to the
nomenclature of the United States Navy), are given in the following table, which
16
INSTRUMENTS AND ACCESSORIES IN NAVIGATION.
shows also the degrees, minutes, and seconds from North or South to which each
division corresponds:
Points.
Angular
measure.
Points.
Angular
measure.
NORTH TO EAST.
Nnrlh-
/ //
EAST TO SOUTH.
East.
8
90 00 00
N 1 E
1
2 48 45
E.-JS
8J
92 48 45
N | E
5 37 30
E. IS
8J
95 57 30
N E
1
8 26 15
E. f S
8|
98 26 15
N bv E
1
11 15 00
E. byS...
9
101 15 00
N hv E 4 E
14 03 45
ESE. f E . .
91
104 03 45
N byE }E
14
16 52 30
ESE.iE
91
106 52 30
N by E E
if
19 41 15
ESE. IE
9|
109 41 15
NNE
2
22 30 00
ESE
10
112 30 00
NNE E
21
25 18 45
SE. byE. fE
101
115 18 45
NNE $ E
2*
28 07 30
SE. byE. |E
101
118 07 30
NNE f E
2i
30 56 15
SE. byE. IE...
id
320 56 15
NE by N
3
33 45 00
SE. by E
11
123 45 00
NE. f N
31
36 33 45
SE. |E
111
126 33 45
NE. 1 N
3f
39 22 30
SE.^E
111
129 22 30
NE 1 N
3J
42 11 15
SE. IE
llf
13^ 11 15
NE
4
45 00 00
SE
12
135 00 00
NE E
41
47 48 45
SE 1 S
121
137 48 45
NE A E
41
50 37 30
SE S
12i
140 37 30
NE f E
4J
53 26 15
SE | S
12
143 26 15
NE byE
5
56 15 00
SE by S
13
146 15 00
NE by E 1 E
51
59 03 45
SSE E
131
149 03 45
NE byE. IE
5A
61 52 30
SSE. * E .
m
151 52 30
NE byE. IE
53
64 41 15
SSE. 1 E .
13f
154 41 15
ENE
6
67 30 00
SSE
14
157 30 00
ENE i E
61
70 18 45
S by E f E
141
160 18 45
ENE i E
6f
73 07 30
S by E ^ E
14!
163 07 30
ENE. IE..
S|
75 56 15
S by E IE
LU Z
14 1
165 56 15
E.byN
7
78 45 00
S byE
15
168 45 00
E N
71
81 33 45
S 4 E
151
171 33 45
E $N
71
84 2? 30
S i E
151
174 " 30
E JN
7i
87 11 15
S i E
15?
177 11 15
SOUTH TO WEST.
WEST TO NORTH.
West
24
270 00 00
South
16
180 00 00
WIN
241
272 48 45
S.I W
161
182 48 45
W N
241
275 37 30
S. * W
161
185 37 30
W f N
24J
278 9 6 15
S.fW
16J
188 26 15
W by N
25
281 15 00
S. byW
17
191 15 00
WNW W
251
284 03 45
S.byW.JW
171
194 03 45
WNW ^W
251
286 52 30
S. byW. *W
17*
196 52 30
WNW 1 W
25J
289 41 15
S.byW.fW..,
17|
199 41 15
WNW
26
292 30 00
ssw
18
202 30 00
NW by W f W
9fil
295 IS 4^
SSW. -JW
181
205 18 45
NW by W \ W
* U 4
261
298 07 30
ssw. ^w
18*
208 07 30
NW byW 1W
262
300 56 15
ssw. * w....
181
210 56 15
NW byW
27
303 45 00
SW. byS
19
213 45 00
NW W
271
306 33 45
SW.f S
191
216 33 45
NW W
27^
309 22 30
SW. *S
191
219 22 30
NW 1 W
27J
311 11 15
SW.-fcS
19|
222 11 15
NW
28
315 00 00
SW
20
225 00 00
NW 1 N
281
317 48 45
SW. 1W
201
227 48 45
NW 1 N
9 81
320 37 30
SW. *W
201
230 37 30
NW N
9 8f
393 26 15
SW. | W
201
233 26 15
NW by N
99
326 15 00
SW. byW...
21
2o6 15 00
NNW W
291
329 03 45
Sw.byW.iW..
211
2o9 03 45
NNW 1 W
291
331 52 30
SW. by W. W
21*
241 52 30
NNW 1 W
29$
334 41 15
SW. by W. 2 W
21|
244 41 15
NNW
30
337 30 00
WSW
22
247 30 00
NV>v W 3. W
cmi
340 1^4^
WSW.iW....
22J
250 18 45
N by W 1 W
Qfii
343 07 30
WSW. *W
22i
253 07 30
N "by W 1 W
30f
345 5(j 15
WSW. W..
22|
255 56 15
N byW
31
348 45 00
W.bvS
23
258 45 00
N W
311
351 33 45
W.f S
231
261 33 45
N 4 W
311
354 " 30
W.-fcS
O of
23*,
264 22 30
N 1 W
Qli
357 n 15
W.-JS
23
267 11 15
North
3 9
3fiO 00 00
INSTRUMENTS AND ACCESSORIES IN NAVIGATION. 17
28. The compass card is mounted in a bowl which is carried in gimbals, thus
enabling the card to retain a horizontal position while the ship is pitching and rolling.
A vertical black line called the lubber s line is marked on the inner surface of the bowl,
and the compass is so mounted that a line joining its pivot with the lubber s fine is
parallel to the keel line of the vessel; thus the lubber s line always indicates the com
pass direction of the ship s head.
29. According to the purpose which it is designed to fulfill, a compass is desig
nated as a Standard, Steering, Check, or Boat Compass. On United States naval ves
sels additional compasses are designated as follows: Maneuvering, battle, auxiliary
battle, top, and conning-tower compasses.
30. There are two types of magnetic compass in use, the liquid or wet and the
dry; in the former the bowl is filled with liquid, the card being thus partially buoyed
with consequent increased ease of working on the pivot, and the liquid further serving
to decrease the vibrations of the card when deflected by reason 01 the motion of the
vessel or other cause. On account of its advantages the liquid compass is used in
the United States Navy.
31. THE NAVY SERVICE T^-INCH LIQUID COMPASS. This consists of a skeleton
card 7i inches in diameter, made of tinned brass, resting on a pivot in liquid, with
provisions for two pairs of magnets symmetrically placed.
The magnet system of the card consists of four cylindrical bundles of steel wires;
these wires are laid side by side and magnetized as a bundle between the poles of a
powerful electro-magnet. They are afterwards placed in a cylindrical case, sealed,
and secured to the card. Steel wires made up into a bundle were adopted because
they are more homogeneous, can be more perfectly tempered, and for the same weight
give greater magnetic power than a solid steel bar.
Two of the magnets are placed parallel to the north and south diameter of the
card, and on the chords of 15 (nearly) of a circle passing through their extremities.
These magnets penetrate the air vessel, to which they are soldered, and are further
secured to the bottom of the ring of the card. The other two magnets of the system
are placed parallel to the longer magnets on the chords of 45 (nearly) of a circle
passing through their extremities and are secured to the bottom of the ring of the card.
The card is of a curved annular type, the outer ring being convex on the upper
and inner side, and is graduated to read to one-quarter point, a card circle being
adjusted to its outer edge and divided to half degrees, with legible figures at each
3, for use in reading bearings by an azimuth circle or in laving the course to degrees.
The card is provided with a concentric spheroidal air vessel, to buoy its own
weight and that of the magnets, allowing a pressure of between 60 and 90 grains on
the pivot at 60 F.; the weight of the card in air is 3,060 grains. The air vessel has
within it a hollow cone, open at its lower end, and provided with the pivot bearing
or cap, containing a sapphire, which rests upon the pivot and thus supports the
card; the cap is provided with adjusting screws for accurately centering the card.
The pivot is fastened to the center of the bottom of the bowl by a flanged plate and
screws. Through this plate and the bottom of the bowl are two small holes which
communicate with the expansion chamber and admit of a circulation of the liquid
between it and the bowl. The pivot is of gun metal with an iridium cap.
The card is mounted in a bowl of cast bronze, the glass cover of which is closely
packed with rubber, preventing the evaporation or leakage of the liquid, which entirely
nils the bowl. This liquid is composed of 45 per cent pure alcohol and 55 per cent
distilled water, and remains liquid below 10 F.
The lubber s line is a fine line drawn on an enameled plate on the inside of the
bowl, the inner surface of the latter being covered with an insoluble white paint.
Beneath the bowl is a metallic self-adjusting expansion chamber of elastic metal,
by means of which the bowl is kept constantly full without the show of bubbles or the
development of undue pressure caused by the change in volume of the liquid due
to changes of temperature.
The rim of the compass bowl is made rigid and its outer edge turned strictly
to gauge to receive the azimuth circle.
32. THE DRY COMPASS. The Lord Kelvin Compass, which may be regarded
as the standard for the dry type, consists of a strong paper card with the
central parts cut away and its outer edge stiffened by a thin aluminum ring. The
61828]
20 INSTRUMENTS AND ACCESSORIES IN NAVIGATION.
standard compass being located, all peloruses may be oriented from it by any one
of the following methods :
(a) By making the azimuth of a celestial body, taken by the pelorus, coincide
with the simultaneous azimuth of the same body taken by the standard compass.
(b) By a similar process with distant objects; and the parallax may be entirely
eliminated in an apparently near object, in view of the moderate distance that
usually separates the two instruments on board ship.
(c) By reciprocal bearings between the correct instrument and the instrument
to be established; it is evident that if the lubber lines of the two instruments are
both in the direction of the keel line, the bearing of the sight vane of each from the
other (one being reversed) should coincide.
(d) By computing the angle subtended at the pelorus by the fore-and-aft line
through the pelorus and the line drawn through the pelorus to the jack staff, and
setting the pelorus at this angle and sighting on the jack staff.
THE CHART.
37. A nautical chart is a miniature representation upon a plane surface, in
accordance with a definite system of projection or development, 01 a portion of the
navigable waters of the world. It generally includes the outline of the adjacent
land, together with the surface forms and artificial features that are useful as aids
to navigation, and sets forth the depths of water, especially in the near approaches
to the land, by soundings that are fixed in position by accurate determinations.
Except in charts of harbors or other localities so limited that the curvature of the
earth is inappreciable on the scale of construction, a nautical chart is always framed
over with a network of parallels of latitude and meridians of longitude in relation
to which the features to be depicted on the chart are located and drawn; and the
mathematical relation between the meridians and parallels of the chart and those
of the terrestrial sphere determines the method of measurement that is to be employed
on the chart and the special uses to which it is adapted.
38. There are three principal systems of projection in use: (a) the Mercator,
(b) the poly conic, and (c) the gnomonic; of these the Mercator is byf ar the most generally
used for purposes of navigation proper, while the polyconic and the gnomonic charts
are employed for nautical purposes in a more restricted manner, as for plotting
surveys or for facilitating great circle sailing.
39. THE MERCATOR PROJECTION. The Mercator Projection, so called, may be
said to result from the development, upon a plane surface, of a cylinder which is
tangent to the earth at the equator, the various points of the earth s surface having
been projected upon the cylinder in such manner that the loxodromic curve or
rhumb line (art. 6, Chap. I) appears as a right line preserving the same angle of
bearing with respect to the intersected meridians as does the ship s track.
In order to realize this condition, the line of tangency, which coincides with the
earth s equator, being the circumference of a right section of the cylinder, will appear
as a right ^line on the development; while the series of elements of the cylinder
corresponding to the projected terrestrial meridians will appear as equidistant right
lines, parallel to each other and perpendicular to the equator of the chart, main
taining the same relative positions and the same distance apart on that equator as
the meridians have on the terrestrial spheroid. The series of terrestrial parallels
will also appear as a system of right lines parallel to each other and to the equator,
and will so^intersect the meridians as to form a system of rectangles whose altitudes,
for successive intervals of latitude, must be variable, increasing from the equator in
such manner that the angles made by the rhumb line with the meridian on the chart
may maintain the required equality with the corresponding angles on the spheroid.
, 40. MERIDIONAL PARTS. At the equator a degree of longitude is equal to a
degree of latitude^ but in receding from the equator and approaching the pole, while
the degrees of latitude remain always of the same length (save for a slight change
due to the fact that the earth is not a perfect sphere), the degrees of longitude become
less and less.
Since, in the Mercator projection, the degrees of longitude are made to appear
everywhere of the same length, it becomes necessary, in order to preserve the propor-
INSTRUMENTS AND ACCESSOKIES IN NAVIGATION. 21
tion that exists at different parts of the earth s surface between degrees of latitude
and degrees of longitude, that the former be increased from their natural lengths,
and such increase must become greater and greater the higher the latitude.
The length of the meridian, as thus increased, between the equator and any
given latitude, expressed in minutes at the equator as a unit, constitutes the number
of Meridional Parts corresponding to that latitude. The Table of Meridional Parts
or Increased Latitudes (Table 3), computed for every minute of latitude between
and 80, affords facilities for constructing charts on "the Mercator projection and for
solving problems in Mercator sailing.
41. To CONSTRUCT A MERCATOR CHARTS If the chart for which a projection
is to be made includes the equator, the values to be measured off are given directly
by Table 3. If the equator does not come upon the chart, then the parallels of
latitude to be laid down should be referred to a principal parallel, preferably the lowest
parallel to be drawTi on the chart. The distance of any other parallel of latitude
from the principal parallel is then the difference of the values for the two taken from
Table 3.
The values so found may either be measured off, without previous numerical
conversion, by means of a diagonal scale constructed on the chart, or they may be
laid dowTi on the chart by means of any properly divided scale of yards, meters, feet,
or miles, after having been reduced to the scale of proportions adopted for the chart.
If, for example, it be required to construct a chart on a scale of one-quarter of an
inch to five minutes of arc on the equator, a diagonal scale may first be constructed,
on which ten meridional parts, or ten minutes of arc on the equator, have a length
of half an inch.
It may often be desirable to adapt the scale to a certain allotment of paper. In
this case, the lowest and the highest parallels of latitude may first be drawn on the
sheet on which the transfer is to be made. The distance oetween these parallels
may then be measured, and the number of meridional parts between them ascertained.
Dividing the distance by this number will then give the length of one meridional
part, or the quantity by which all the meridional parts taken from Table 3 must be
multiplied. This quantity will represent the scale of the chart. If it occurs that the
limits of longitude are a governing consideration, the case may be similarly treated.
EXAMPLE: Let a projection be required for a chart of 14 extent in longitude
between the parallels of latitude 20 30 and 30 25 , and let the space allowable on
the paper between these parallels measure 10 inches.
Entering the column in Table 3 headed 20, and running down to the line marked
30 in the side column, will be found 1248.9; then, entering the column 30, and
running dowTi to the line 25 , will be found 1905.5. The difference, or 1905.5
1248.9 = 656.6, is the value of the meridional arc between these latitudes, for which
1 of arc of the equator is taken as the unit. On the intended projection, therefore,
10 in
I 7 of arc of longitude will measure .,. =0.0152 inch, which will be the scale of the
o5o.b
chart. For the sake of brevity call it 0.015. By this quantity all the values derived
from Table 3 will have to be multiplied before laying them down on the projection, if
they are to be measured on a diagonal scale of one inch.
Draw in the center of the sheet a straight line, and assume it to be the middle
meridian of the chart. Construct very carefully on this line a perpendicular near
the lower border of the sheet, and assume this perpendicular to be the parallel of
latitude 20 30 ; this will be the southern inner neat line of the chart. From the
intersection of the lines lay off on the parallel, on each side of the middle meridian,
seven degrees of longitude, or distances each equal to 0.015X60X7 = 6.3 inches;
and through the points thus obtained draw lines parallel to the middle meridian,
and these will be the eastern and western neat lines of the chart.
In order to construct the parallel of latitude for 21 00 , find, in Table 3, the
meridional parts for 21 00 , which are 1280.8. Subtracting from this number the
number for 20 30 , and multiplying the difference by 0.015, we obtain 0.478 inch,
which is the distance on the chart between 20 30 and 21 00 . On the meridians
a This construction for the purpose of plotting lines of position in ordinary navigation will often be unnecessary if use is
made of the Position Plotting Sheets published by the Hydrographic Office.
20 INSTRUMENTS AND ACCESSORIES IN NAVIGATION.
standard compass being located, all peloruses may be oriented from it by any one
of the following methods :
(a) By making the azimuth of a celestial body, taken by the pelorus, coincide
with the simultaneous azimuth of the same body taken by the standard compass.
(&) By a similar process with distant objects; and the parallax may be entirely
eliminated in an apparently near object, in view of the moderate distance that
usually separates the two instruments on board ship.^
(c) By reciprocal bearings between the correct instrument and the instrument
to be established; it is evident that if the lubber lines of the two instruments are
both in the direction of the keel line, the bearing of the sight vane of each from the
other (one being reversed) should coincide.
(d) By computing the angle subtended at the pelorus by the fore-and-aft line
through the pelorus and the line drawn through the pelorus to the jack staff, and
setting the pelorus at this angle and sighting on the jack staff.
THE CHART.
37. A nautical chart is a miniature representation upon a plane surface, in
accordance with a definite system of projection or development, of a portion of the
navigable waters of the world. It generally includes the outline of the adjacent
land, together with the surface forms and artificial features that are useful as aids
to navigation, and sets forth the depths of water, especially in the near approaches
to the land, by soundings that are fixed in position by accurate determinations.
Except in charts of harbors or other localities so limited that the curvature of the
earth is inappreciable on the scale of construction, a nautical chart is always framed
over with a network of parallels of latitude and meridians of longitude in relation
to which the features to be depicted on the chart are located and drawn; and the
mathematical relation between the meridians and parallels of the chart and those
of the terrestrial sphere determines the method of measurement that is to be employed
on the chart and the special uses to which it is adapted.
38. There are three principal systems of projection in use: (a) the Mercator,
(&) the poly conic, and (c) the gnomonic; of these the Mercator is byf ar the most generally
used for purposes of navigation proper, while the polyconic and the gnomonic charts
are employed for nautical purposes in a more restricted manner, as for plotting
surveys or for facilitating great circle sailing.
39. THE MERCATOR PROJECTION. The Mercator Projection, so called, may be
said to result from the development, upon a plane surface, of a cylinder which is
tangent to the earth at the equator, the various points of the earth s surface having
been projected upon the cylinder in such manner that the loxodromic curve or
rhumb line (art. 6, Chap. I) appears as a right line preserving the same angle of
bearing with respect to the intersected meridians as does the ship s track.
In order to realize this condition, the line of tangency, which coincides with the
earth s equator, being the circumference of a right section of the cylinder, will appear
as a right line on the development; while the series of elements of the cylinder
corresponding to the projected terrestrial meridians will appear as equidistant right
lines, parallel to each other and perpendicular to the equator of the chart, main
taining the same relative positions and the same distance apart on that equator as
the meridians have on the terrestrial spheroid. The series of terrestrial parallels
will also appear as a system of right lines parallel to each other and to the equator,
and will so^intersect the meridians as to form a system of rectangles whose altitudes,
for successive intervals of latitude, must be variable, increasing from the equator in
such manner that the angles made by the rhumb line with the meridian on the chart
may maintain the required equality with the corresponding angles on the spheroid.
, 40. MERIDIONAL PARTS. At the equator a degree of longitude is equal to a
degree of latitude^ but in receding from the equator and approaching the pole, while
the degrees of latitude remain always of the same length (save for a slight change
due to the fact that the earth is not a perfect sphere), the degrees of longitude become
less and less.
Since, in the Mercator projection, the degrees of longitude are made to appear
everywhere of the same length, it becomes necessary, in order to preserve the propor-
INSTRUMENTS AND ACCESSORIES IN NAVIGATION. 21
tion that exists at different parts of the earth s surface between degrees of latitude
and degrees of longitude, that the former be increased from their natural lengths,
and such increase must become greater and greater the higher the latitude.
The length of the meridian, as thus increased, between the equator and any
given latitude, expressed in minutes at the equator as a unit, constitutes the number
of Meridional Parts corresponding to that latitude. The Table of Meridional Parts
or Increased Latitudes (Table 3), computed for every minute of latitude between
and 80, affords facilities for constructing charts on the Mercator projection and for
solving problems in Mercator sailing.
41. To CONSTRUCT A MERCATOR CHART. If the chart for which a projection
is to be made includes the equator, the values to be measured off are given directly
by Table 3. If the equator does not come upon the chart, then the parallels of
latitude to be laid down should be referred to a principal parallel, preferably the lowest
Earallel to be drawn on the chart. The distance of any other parallel of latitude
*om the principal parallel is then the difference of the values for the two taken from
Table 3.
The values so found may either be measured off, without previous numerical
conversion, by means of a diagonal scale constructed on the chart, or they may be
laid down on the chart by means of any properly divided scale of yards, meters, feet,
or miles, after having been reduced to the scale of proportions adopted for the chart.
If, for example, it be required to construct a chart on a scale of one-quarter of an
inch to five minutes of arc on the equator, a diagonal scale may first be constructed,
on which ten meridional parts, or ten minutes of arc on the equator, have a length
of half an inch.
It may often be desirable to adapt the scale to a certain allotment of paper. In
this case, the lowest and the highest parallels of latitude may first be drawn on the
sheet on which the transfer is to be made. The distance between these parallels
may then be measured, and the number of meridional parts between them ascertained.
Dividing the distance by this number will then give the length of one meridional
part, or the quantity by which all the meridional parts taken from Table 3 must be
multiplied. This quantity will represent the scale of the chart. If it occurs that the
limit.fi of longitude are a governing consideration, the case may be similarly treated.
EXAMPLE: Let a projection be required for a chart of 14 extent in longitude
between the parallels of latitude 20 30 and 30 25 , and let the space allowable on
the paper between these parallels measure 10 inches.
Entering the column in Table 3 headed 20, and running down to the line marked
30 in the side column, will be found 1248.9; then, entering the column 30, and
running down to the line 25 , will be found 1905.5. The difference, or 1905.5
1248.9 = 656.6, is the value of the meridional arc between these latitudes, for which
I of arc of the equator is taken as the unit. On the intended projection, therefore,
10 in
1 of arc of longitude will measure -_ =0.0152 inch, which will be the scale of the
DOO.D
chart. For the sake of brevity call it 0.015. By this quantity all the values derived
from Table 3 will have to be multiplied before laying them down on the projection, if
they are to be measured on a diagonal scale of one inch.
Draw in the center of the sheet a straight line, and assume it to be the middle
meridian of the chart. Construct very carefully on this line a perpendicular near
the lower border of the sheet, and assume this perpendicular to be the parallel of
latitude 20 30 ; this will be the southern inner neat line of the chart. From the
intersection of the lines lay off on the parallel, on each side of the middle meridian,
seven degrees of longitude, or distances each equal to 0.015X60X7 = 6.3 inches;
and through the points thus obtained draw lines parallel to the middle meridian,
and these will be the eastern and western neat lines of the chart.
In order to construct the parallel of latitude for 21 00 , find, in Table 3, the
meridional parts for 21 00 , which are 1280.8. Subtracting from this number the
number for 20 30 , and multiplying the difference by 0.015, we obtain 0.478 inch,
which is the distance on the chart between 20 30 and 21 00 . On the meridians
a This construction for the purpose of plotting lines of position in ordinary navigation will often be unnecessary if use is
made of the Position Plotting Sheets published by the Hydrographic Office.
22 INSTRUMENTS AND ACCESSORIES IN NAVIGATION.
lay off distances equal to 0.478 inch, and through the three points thus obtained
draw a straight line, which will be the parallel of 21 00 .
Proceed in the same manner to lay down all the parallels answering to full
degrees of latitude; the distances will be respectively:
O in .015X (1344.9- 1248.9) = 1.440 inches.
O in .015 X (1409.5 - 1248.9) = 2.409 inches.
O in . 105 X (1474.5 -1248.9) =3.384 inches, etc.
Thus will be shown the parallels of latitude 22 00 , 23 0<X, 24 00 , etc. FinaUy,
lay down in the same way the parallel of latitude 30 25 , which will be the northern
inner neat line of the chart.
A degree of longitude will measure on this chart O in .015X60 = O in .9. Lay off,
therefore, on the lowest parallel of latitude drawn on the chart, on a middle one, and
on the highest parallel, measuring from the middle meridian toward each side, the
distances of O in .9, l in .8, 2 in .7, 3 in .6, etc., in order to determine the points where
meridians answering to full degrees cross the parallels drawn on the chart. Through
the points thus found draw the meridians. Draw then the outer neat lines of the
chart at a convenient distance outside of the inner neat lines, and extend to them the
meridians and parallels. Between the inner and outer neat lines of the chart sub
divide the degrees of latitude and longitude as minutely as the scale of the chart will
permit, the subdivisions of the degrees of longitude being found by dividing the
degrees into equal parts, and the subdivisions of the degrees of latitude being accu
rately found in the same manner as the full degrees of latitude previously described,
though it will generally be found sufficiently exact to make even subdivisions of the
degrees, as in the case of the longitude.
The subdivisions between the two eastern as well as those between the two
western neat lines will serve for measuring or estimating terrestrial distances. Dis
tances between points bearing North and South of each other may be ascertained
by referring them to the subdivisions between the same parallels. Distances repre
sented by fines at an angle to the meridians (loxodromic lines) may be measured
by taking between the dividers a small number of the subdivisions near the middle
latitude of the line to be measured, and stepping them off on that line. If, for
instance, the terrestrial length of a line running at an angle to the meridians between
the parallels of latitude of 24 00 and 29 00 be required, the distance shown on the
neat space between 26 15 and 26 45 ( = 30 nautical miles) may be taken between
the dividers and stepped off on that line.
42. Coast lines and other positions are plotted on the chart by their latitude
and longitude. A chart may be transferred from any other projection to that of
Mercator by drawing a system of corresponding parallels of latitude and meridians
over both charts so close to each other as to form minute squares, and then the lines
and characters contained in each square of the map to be transferred may be copied
by the eye in the corresponding squares of the Mercator projection.
Since the unit of measure, the mile or minute of latitude, has a different value
in every latitude, there is an appearance of distortion in a Mercator chart that covers
any large extent of surface; for instance, an island near the pole will be represented
as being much larger than one of the same size near the equator, due to the different
scale used to preserve the character of the projection.
43. THE POLYCONIC PROJECTION. This projection is based upon the develop
ment of the earth s surface on a series of cones, a different one for each parallel of
latitude, each one having the parallel as its base, and its vertex in the point where a
tangent to the earth at that latitude intersects the earth s axis. The degrees of
latitude and longitude on this chart are projected in their true length, and the general
distortion of the figure is less than in any other method of projection, the relative
magnitudes being closely preserved.
A straight line on the polyconic chart represents a near approach to a great
circle, making a slightly different angle with each successive meridian as the meridians
converge toward the pole and are theoretically curved lines; but it is only on charts
of large extent that this curvature is apparent; the parallels are also curved, this
fact being apparent to the eye upon all excepting the largest scale charts.
INSTRUMENTS AND ACCESSORIES IN NAVIGATION.
23
This method of projection is especially adapted to the plotting of surveys; it
is also employed to some extent in the charts of the United States Coast and Geodetic
Survey.
44. GXOMONIC PROJECTION. This is based upon a system in which the plane
of projection is tangent to the earth at some given point; the eye of the spectator
is situated at the center of the sphere, where, being at once in the plane of every great
circle, it will see all such circles projected as straight lines where the visual rays
passing through them intersect tie plane of projection. In a gnomonic chart, tne
straight line between any two points represents the arc of a great circle, and is there
fore the shortest line between those points.
Excepting in the polar regions, for which latitudes the Mercator projection can
not be constructed, the gnomonic charts are not used for general navigating purposes.
Their greatest application is to afford a ready means of finding the course and distance
at any time in great circle sailing, the method of doing which will be explained in
Chapter V.
45. MERIDIANS ADOPTED IN THE CONSTRUCTION OF CHARTS. The nautical
charts published by the United States are based upon the meridian of Greenwich,
and this meridian is also the origin of longitudes in use on the nautical charts pub
lished by the Governments of Argentina, Austria, Belgium, Brazil, Chile, Denmark,
France, Germany, Great Britain, Holland (for all charts published at Batavia and
for some published at The Hague), Italy, Japan, Norway, Kussia, and Sweden.
In addition to the meridian of Greenwich, the meridian of Pulkowa Observatory,
at St. Petersburg, in longitude 30 19 40" east of Greenwich, is sometimes referred
to in the Kussian charts. At one time the Royal Observatory at Naples, in longitude
14 15 26" east of Greenwich, was referred to in the Italian charts, and the observatory
at Christiania, in longitude 10 43 23" east of Greenwich, was referred to in the
Norwegian charts.
The French charts are based both upon the meridian of Greenwich and of the
Observatory at Paris, which has been determined to be in longitude 2 20 14.6" east
of Greenwich. The longitudes of a few Dutch charts published at The Hague are
reckoned from the meridian of the west tower of the cathedral at Amsterdam, which
is hi longitude 4 53 01.5" east of Greenwich. Portuguese charts refer to the meridian
of the observatory of Lisbon Castle, which is 9 07 54.86" west of Greenwich, and
to the meridian of Greenwich. In Spain the meridian of San Fernando Observatory,
at Cadiz, which is in longitude 6 12 20" west of Greenwich, and also the meridian
of Greenwich, are used.
46. QUALITY OF BOTTOM. The following table shows the qualities of the
bottom, as expressed on charts of various nations:
United States.
English.
French.
Italian.
Spanish.
German.
Clay C.
Clay cl.
Argile A.
Argila arg.
Arcillo or Barro.arc.
Lehm L.
Coral Co.
Coral c r l
Corail Cor
Corallo crl
Coral cl
Ko T "allen Kor.
Gravel G
Gravel g
Gravier Gr
Rena or Ghia a gh
Cases jo Co
Ivies k
Mud. M
Mud m
Vase V
Fango f
Fango or Luno F
RnhlamTn Schl.
Rocky rky.
Rock rk.
Roche... R.
Roccia r.
PiedraorRoca P.orr.
Felsig Fls.
Sand S
Sand s
Sable S
Sfibbiaor Vena s
\rpna -V
Sand Sd.
Shells Sh
Shells sh
Coquille Coq
Muscheln M
Stone St
Stones st
Pierre P
Pietre p
Piedra P
Stein St.
Weed Wd
Weed wd
Kerb II
Alga V
Gras Grs
Fine fne
Fine f
Fin fir.
Fino
Fina f
Fein f.
Coarse crs.
Coarse c
Gros g
Grosso
Gruesa
Grob . gb.
Stiff stf.
Stiff stf.
Dure.. d.
Tenace.
Tena?
Schlick sk.
Soft sft.
Soft sff
Voile ni
Molle
Blando bclo
Welch Wch.
Black.. bk
Black blk
Nero
Schwarz sch\v.
Red rd.
Red. rd
Rou^e r
Rosse
Rojo r
Roth r.
Yellow... yl
Yellow v
Jaune j
Giallo
\marillo am
Gelb.... g.
Gray . . ev
24
INSTRUMENTS AND ACCESSORIES IN NAVIGATION.
47. MEASURES OF DEPTH. The following table shows the units of measure
employed in expressing the soundings in the more modern nautical charts of foreign
nations together with their equivalents in the units of measure used in the charts
published by the United States :
Nationality of
chart.
Unit of soundings.
Equivalent in United
States units.
Nationality of
chart.
Unit of soundings.
Equivalent in United
States units.
Feet.
3.281
3.281
6.223
3. 281
3.281
6.176
5.905
3.281
3.281
3.281
3.281
Fathoms.
Feet.
Fathoms.
Argentine...
Austrian
Belgian
Metro
0.547
0.547
1.037
0.547
0.547
1.029
0.984
0.547
0.547
0.547
0.547
Japanese
Norwegian
Fathom
6.000
3.281
6.176
3.281
6.000
3.281
5.492
3.281
5.844
6.000
1.000
0.547
1.029
0.547
1.000
0.547
0.914
0.547
0.974
1.000
Metro
Metre
or faden
Portuguese. .
Russian
or favn
Metre
Metro
Metro .
Chilean
Danish.
Dutch
Sajene
favn
vadem
Spanish
Metro
Swedish. . .
or braza
French
or metre
Metre
Metre
British
or famn
Fathom..
German .
do..
Italian
1
Metro
THE BAROMETER.
48. The barometer is an instrument for measuring the pres
sure of the atmosphere, and is of great service to the mariner
in affording a knowledge of existing meteorological conditions
and of the probable changes therein. There are two classes of
barometer mercurial and aneroid.
49. THE MERCURIAL BAROMETER. This instrument, in
vented by Torricelli in 1643, indicates the pressure of the atmos
phere by the height of a column of mercury.
If a glass tube of uniform internal diameter somewhat
more than 30 inches in length and closed at one end be com
pletely^ filled with pure mercury, and then placed, open end
down, in a cup of mercury (the open end having been tempo
rarily sealed to retain the liquid during the process of inverting),
it will be found that the mercury in the tube will fall until the
top of the column is about 30 inches above the level of that
which is in the cup, leaving in the upper part of the tube a
vacuum. Since the weight of the column of mercury thus left
standing in the tube is equal to the pressure by which it is held
WISP! HI * n P os ^ on nam ely, that of the atmospheric air it follows that
the height of the column is subject to variation upon variation of
that pressure; hence the mercury falls as the pressure of the
atmosphere decreases and rises as that pressure increases. The
mean pressure of the atmosphere is equal to nearly 15 pounds
to the square inch; the mean height of the barometer is about
30 inches.
50. In the practical construction of the barometer the glass
tube which contains the mercury is encased in a brass tube, the
latter terminating at the top in a ring to be used for suspension,
and at the bottom in a flange, to which the several parts form
ing the cistern are attached. The upper part of the brass
tube is partially cut away to expose the mercurial column for
observation; abreast this opening is fitted a scale for measur
ing the height, and along the scale travels a vernier for exact
reading; the motion of the vernier is controlled by a rack and
pinion, the latter having a milled head accessible to the observer,
FIG. 3. by which the adjustment is made. In the middle of the brass FIG. 4.
tube is fixed a thermometer, the bulb of which is covered from
the outside but open toward the mercury, and which, being nearly in contact with
the glass tube, indicates the temperature of the mercury and not that of the external
INSTRUMENTS AND ACCESSORIES IN NAVIGATION.
25
air; the central position of the column is selected in order that the mean temperature
may be obtained a matter of importance, as the temperature of the mercurial
column must be taken into account in every accurate application of its reading.
51. In the arrangement of further details mercurial barometers are divided
into two classes, according as they are to be used, as Standards (fig. 4) on shore, or
as Sea Barometers (fig. 3) on shipboard.
In the Standard Barometer the scale and vernier are so graduated as to enable
an observer to read the height of the mercurial column to the nearest 0.002 inch,
while in the Sea Barometer the reading can not be made closer than 0.01 inch.
The instruments also differ in the method of obtaining the true height of the
mercurial column at varying levels of _ the liquid in the cistern. It is evident that
as the mercury in the tube rises, upon increase of atmospheric pressure, the mercury
in the cistern must fall; and, conversely, when the mercurial column falls the amount
of fluid in the cistern will thereby be increased and a rise of level will occur. As the
height of the mercurial column is required above the existing level in the cistern,
some means must be adopted to obtain the true height under varying conditions.
In the Standard Barometer the mercury of the cistern is contained in a leather bag,
against the bottom of which presses the point of a vertical screw, the milled head
of the screw projecting from the bottom of the instrument and thus placing it under
control of the observer. By this means the surface of the mercury in the cistern
(which is visible through a glass casing) may be raised or lowered until it exactly
coincides with that level which is chosen as the zero of the scale, and which is indicated
by an ivory pointer in plain view.
In the Sea Barometer there is no provision for adjusting the level of the cistern
to a fixed point, but compensation for the variable level is made in the scale gradu
ations ; a division representing an inch on the scale is a certain fraction short of the
true inch, proper allowance being thus made for the rise in level which occurs with
a fall of the column, and for the reverse condition.
Further modification is made in the Sea Barometer to adapt it to the special
use for which intended. The tube toward its lower end is much contracted to prevent
the oscillation of the mercurial column known as "pumping," which arises from the
motion of the ship ; and just below this point is a trap to arrest anv small bubbles
of air from finding their way upward. The instrument aboard ship is suspended in
a revolving center ring, in gimbals, supported on a horizontal brass arm which is
screwed to the bulkhead; a vertical position is thus maintained by the tube at all
times.
52. The vernier is an attachment for facilitating the exact reading of the scale
of the barometer, and is also applied to many other instruments of precision, as, for
example, the sextant and theodolite. It consists of a metal scale similar
in general construction to that of the instrument to which it is fitted, and
arranged to move alongside of and in contact with the main scale.
The general principle of the vernier requires that its scale shall have
a total length exactly equal to some whole number of divisions of the scale
of the instrument and tnat this length shall be subdivided into a number
of parts equal to 1 more or 1 less than the number of divisions of the
instrument scale which are covered; thus, if a space of 9 divisions of the
main scale be designated as the length of the vernier, the vernier scale
would be divided into either 8 or 10 parts.
Suppose that a barometer scale be divided into tenths of an inch and
that ^ a length of 9 divisions of such a scale be divided into 10 parts for a
vernier (fig. 5) ; and suppose that the divisions of the vernier be numbered
consecutively from zero at the origin to 10 at the upper extremity^. If, now,
by means of the movable rack and pinion, the.bottom or zero division of the
vernier be brought level with the top of the mercurial column, and that
division falls into exact coincidence with a division of the main scale, then
the height of the column will correspond with the scale reading indicated.
In such a case the top of the vernier will also exactly coincide with a
scale division, but none of the intermediate divisions will be evenly abreast FIG. 5.
of such a division; the division marked "I" will fall short of a scale
division by one-tenth of 1 division of the scale, or by 0.01 inch ; that marked "2" by
two-tenths of a division, or 0.02 inch; and so on. If the vernier, instead of having
26
INSTRUMENTS AND ACCESSORIES IN NAVIGATION.
the zero coincide with a scale division, has the division " 1 " in such coincidence,
it follows that the mercurial column stands at 0.01 inch above that scale division
which is next below the zero; for the division "2," at 0.02 inch; and similarly for
the others. In the case portrayed in figure 5, the reading of the^column is 29.81
inches, the scale division next below the zero being 29.80 inches, while the fact that
the first division is abreast a mark of the scale shows that 0.01 inch must be added
to this to obtain the exact reading.
Had an example been chosen in which 8 vernier divisions covered 9 scale
divisions that is, where the number of vernier divisions was 1 ^less than the number
of scale divisions covered the principle would still have applied. But, instead of
the length of 1 division of the vernier falling short of a division of the scale by one-
tenth the length of the latter, it would have fallen beyond by one-eighth. To read in
such a case it would therefore be necessary to number the vernier divisions from
up downward and to regard the subdivisions as -fo instead of 0.01 inch.
It is a general rule that the smallest measure to which a vernier reads is equal
to the length of 1 division of the scale divided by the number of divisions of the
vernier; hence, by varying either the scale or the vernier, we may arrive at any
subdivision that may be desired.
53. The Sea Barometer is arranged as described for the instrument assumed in
the illustration; the scale divisions are tenths of an inch, and the vernier has 10
divisions, whence it reads to 0.01 inch. It is not necessary to seek a closer reading,
as complete accuracy is not attainable in observing the height of a barometer on a
vessel at sea, nor is it essential. The Standard Barometer on shore, however, is
capable of very exact reading; hence each scale division is made equal to half a
tenth, or 0.05 inch, while a vernier covering 24 such divisions is divided into 25 parts;
hence the column may be read to 0.002 inch.
54. To adjust the vernier for reading the height of the mercurial column the
eye should be brought exactly on a level with the top of the column; that is, the line
of sight should be at right angles to the scale. When properly set, the front and
rear edges of the vernier and the uppermost point of the mercury should all be in
the line of sight. A piece of white paper, held at the back of the tube so as to reflect
the light, assists in accurately setting the vernier by day, while a small bull s-eye
lamp held behind the instrument enables the observer to get a correct reading at
niojht. When observing the barometer it should hang freely, not being inclined by
holding or even by touch, because any inclination wm cause the column to rise in
the tube.
55. Other things being equal, the mercury will stand higher in the tube when
it is warm than when it is cold, owing to expansion. For the purposes of comparison,
all barometric observations are reduced to a standard which assumes 32 F. as the
temperature of the mercurial column, and 62 F. as that of the metal scale; it is
therefore important to make this reduction, as well as that for instrumental error
(art. 57), in order to be enabled to compare the true barometric pressure with the
normal that may be expected for any locality. The following table gives the value
of this correction for each 2 F., the plus sign showing that the correction is to be
added to the reading of the ship s barometer and the minus sign that it is to be
subtracted:
Tempera
ture.
Correction.
Tempera
ture.
Correction.
Tempera
ture.
Correction.
Tempera
ture.
Correction.
Inch.
Inch..
o
Inch.
Inch.
20
+0.02
40
-0.03
60
-0.09
80
-0. 14
22
+0.02
42
-0.04
62
-0.09
82
-0. 14
24
+0.01
44
-0.04
64
-0.09
84
-0.15
26
+0.01
46
-0.05
66
-0. 10
86
-0. 15
28
0. 00
48
-0. 05
68
-0. 10
88
-0. 16
30
0.00
50
-0.06
70
-0. 11
90
-0.16
32
-0. 01
52
-0.06
72
-0. 12
92
-0.17
34
-0. 02
54
-0. 07
74
-0. 12
94
-0. 17
36
-0.02
56
-0. 07
76
-0. 13
96
-0. 18
38
-0.03
58
-0.08
78
-0.13
98
-0. 18
INSTRUMENTS AND ACCESSORIES IN NAVIGATION. 27
As an example, let the observed reading of the mercurial barometer be 29.95
inches, and the temperature as given by the attached thermometer 74; then we have:
//
Observed height of the mercury 29. 95
Correction for temperature (74) 0. 12
Height of the mercury at standard temperature 29. 83
56. THE ANEROID BAROMETER. This is an instrument in which the pressure
of the air is measured by means of the elasticity of a plate of metal. It consists of a
cylindrical brass box, the metal in the sides being very thin; the contained air having
been partially, though not completely, exhausted, the box is hermetically sealed.
When the pressure of the atmosphere increases the inclosed air is compressed, the
capacity of the box is diminished, and the two flat ends approach each other; when
the pressure of the atmosphere decreases, the ends recede from one another in conse
quence of the expansion of the inclosed air. By means of a combination of levers,
this motion of the ends of the box is communicated to an index pointer which travels
over a graduated dial plate, the mechanical arrangement being such that the motion
of the ends of the box is magnified many times, a very minute movement of the box
making a considerable difference in the indication of the pointer. The graduations
of the aneroid scale are obtained by comparison with the correct readings of a standard
mercurial barometer under normal and reduced atmospheric pressure.
The thermometer attached to the aneroid barometer is merely for convenience
in indicating the temperature of the air, but as regards the instrument itself no cor
rection for temperature can be applied with certainty. Aneroids, as now manufac
tured, are almost perfectly compensated for temperature by the use of different
metals having unequal coefficients of expansion; they ought, therefore, to show the
same pressure at all temperatures.
The aneroid barometer, from its small size and the ease with which it may be trans
ported, can often be usefully employed under circumstances where a mercurial
barometer would not be available. It also has an advantage over the mercurial
instrument in its greater sensitiveness, and the fact that it gives earlier indications
of change of pressure. It can, however, be relied upon only when frequently com
pared with a standard mercurial barometer; moreover, considerable care is required
in its handling; while slight shocks will not ordinarily affect it, a severe jar or knock
may change its indications by a large amount.
When in use the aneroid barometer may be suspended vertically or placed flat,
but changing from one position to another ordinarily makes a sensible change in the
readings; the instrument should always, therefore, be kept in the same position, and
the errors determined by comparisons made while occupying its customary place.
57. COMPARISON OF BAROMETERS. To determine the reliability of the ship s
barometer, whether mercurial or aneroid, comparisons should from time to time be
made with a standard barometer. Nearly all instruments read either too high or too
low by a small amount. These errors arise, in a mercurial barometer, from the
improper placing of the scale, lack of uniformity of caliber of the glass tube, or
similar causes ; in an aneroid, which is less accurate and in which there is even more
necessity for frequent comparisons, errors may be due to derangement of any of the
various mechanical features upon which its working depends. The errors of the
barometer should be determined for various heights, as they are seldom the same at
all parts of the scale.
In the principal ports of the world standard barometers are observed at specified
times each day, and the readings, reduced to zero and to sea level, are published.
It is therefore only necessary to read the barometer on shipboard at those times
and, if a mercurial instrument is used, to note the attached thermometer and apply
the correction for temperature (art. 55). It is evident that a comparison of the
heights by reduced standard and by the ship s barometer will give the correction to
be applied to the latter, including the instrumental error, the reduction to sea level,
and the personal error of the observer. In the United States, standard barometer
readings are made by the Weather Bureau.
Aneroid Barometers may be adjusted for instrumental error by moving the index
hand, but this is usually done only in the case of errors of considerable magnitude.
28 INSTRUMENTS AND ACCESSORIES IN NAVIGATION.
58. DETERMINATION OF HEIGHTS BY BAROMETER. The barometer may be
used to determine the difference in heights between any two stations by means of
the difference in atmospheric pressure between them. An approximate rule is to
allow 0.0011 inch for each difference in level of 1 foot, or, more roughly, 0.01 inch
for every 9 feet.
A very exact method is afforded by Babinet s formula. If B and B represent
the barometric pressure (corrected for all sources of instrumental error) at the lower
and at the upper stations respectively, and t and t the corresponding temperatures of
the air; then,
Diff . in height = C X
if the temperatures be taken by a Fahrenheit thermometer,
C (in feet) =52, 494 (l +
if a centigrade thermometer is used,
C (in meters) = 16,000^1
THE THERMOMETER.
59. The TJiermometer is an instrument for indicating temperature. In its
construction advantage is taken of the fact that bodies are expanded by heat and
contracted by cold. In its most usual form the thermometer consists of a bulb filled
with mercury, connected with a tube of very fine cross-sectional area, the liquid
column rising or falling in the tube according to the volume of the mercury due to the
actual degree of heat, and the height of the mercury indicating upon a scale the
temperature; the mercury contained in the tube moves in a vacuum produced by
the expulsion of the air through boiling the mercury and then closing the top of the
tube by means of the blowpipe.
There are three classes of thermometer, distinguished according to the method
of graduating the scale as follows: the Fahrenheit, in which the freezing point of
water is placed at 32 and its boiling point (under normal atmospheric pressure) at
212; the Centigrade, in which the freezing point is at and the boiling point at
100; and the Reaumur, in which these points are at and 80, respectively. The
Fahrenheit thermometer is generally used in the United States and England. Tables
will be found in this work for the interconversion of the various scale readings
(Table 31).
60. The thermometer is a valuable instrument for the mariner, not only by
reason of the aid it affords him in judging meteorological conditions from the tem
perature of the air and the amount of moisture it contains, but also for the evidences
it furnishes at times, through the temperature of the sea water, of the ship s position
and the probable current that is being encountered.
61. The thermometers employed in determining the temperature of the air
(wet and dry bulb) and of the water at the surface, should be mercurial, and of some
standard make, with the graduation etched upon the glass stem; they should be
compared with accurate standards, and not accepted ii their readings vary more
than 1 from the true at any point of the scale.
INSTRUMENTS AND ACCESSORIES IN NAVIGATION.
29
62. The dry-bulb thermometer gives the temperature of the free air. The
wet-bulb thermometer, an exactly similar instrument, the bulb of \vhich is surrounded
by an envelope of moistened cloth, gives what is known as the temperature of evapora
tion, which is always somewhat less than the temperature of the free air. From the
difference of these two temperatures the observer may determine the proximity of
the air to saturation; that is, how near the air is to that point at which it will be
obliged to precipitate some of its moisture (water vapor) in the form of liquid. With
the envelope of the wet bulb removed, the two thermometers should read precisely
the same; otherwise they are practically useless.
The two thermometers, the wet and the dry bulb, should be hung within a few
inches of each other, and the surroundings should be as far as possible identical. In
practice the two thermometers are gener
ally inclosed within a small lattice case, such
as that shown in figure 6 ; the case should be
placed in a position on deck remote from any
source of artificial heat, sheltered from the
direct rays of the sun, and from the rain and
spray, but freely exposed to the circulation
of the air; the door should be kept closed
except during the process of reading. The
cloth envelope of the wet bulb should be
a single thickness of fine muslin, tightly
stretched over the bulb, and tied with a fine
thread. The wick which serves to carry the
water from the cistern to the bulb should
consist of a few threads of lamp cotton, and
should be of sufficient length to admit of two
or three inches being coiled in the cistern.
The muslin envelope of the wet bulb should
be at all times thoroughly moist, but not
dripping.
When the temperature of the air falls
to 32 F. the water in the wick freezes, the
capillary action is at an end, the bulb in
consequence soon becomes quite dry, and
the thermometer no longer shows the tem
perature of evaporation. At such times the
bulb should be thoroughly wetted with ice-
cold water shortly before the time of observation, using for this purpose a camel s
hair brush or feather; by this process the temperature of the wet bulb is temporarily
raised above that of the dry, but only for a brief time, as the water quickly freezes;
and inasmuch as evaporation takes place from the surface of the ice thus formed
precisely as from the surface of the w r ater, the thermometer will act in the same way
as if it nad a damp bulb. The wet-bulb thermometer can not properly read higher
than the dry, and if the reading of the wet bulb should be the higher, it may always
be attributed to imperfections in the instruments.
o Called a psychrometer.
FIG. G.
30
INSTRUMENTS AND ACCESSORIES IN NAVIGATION.
63. Knowing the temperature of the wet and dry bulbs, the relative humidity
of the atmosphere at the time of observation may be found from the following table :
Tempera
ture of the
Difference between dry-bulb and wet-bulb readings.
i
10
mometer.
1
PC r ct.
Per ct.
Per ct.
Per ct.
Per ct.
Per ct. Per ct.
Per ct. \ Per ct.
Per ct.
24
87
75
62
50
38
26
26
88
76
65
53
42
30
28
89
78
67
56
45
34
24
30
90
79
68
58
48
38
28
32
90
80
70
61
51
41
32
23
34
90
81
72
63
53
44
35
27
36
91
82
73
64
55
47
38
30
22
38
92
83
75
66
57
50
42
34
26
40
92
84
76
68
59
52
44
37
30
22
42
92
84
77
69
61
54
47
40
33
26
44
92
85
78
70
63
56
49
43
36
29
46
93
85
79
72
65
58
51
45
38
32
48
93
80
79
73
66
60
53
47
41
35
50
93
87
80
74
67
61
55
49
43
37
52
94
87
81
75
69
63
57
51
46
40
54
94
88
82
76
70
64
59
53
48
42
56
94
88
82
77
71
65
60
55
50
44
58
94
89
83
78
72
67
61
56
51
46
60
94
89
84
78
73
68
63
58
53
48
62
95
89
84
79
74
69
64
59
54
50
64
95
90
85
79
74
70
65
60
56
51
66
95
90
85
80
75
71
66
61
57
53
68
95
90
85
81
76
71
67
63
58
54
70
95
90
86
81
77
72
68
64
60
55
72
95
91
86
82
77
73
69
65
61
57
74
95
91
86
82
78
74
70
66
62
58
76
95
91
87
82
78
74
70
66
63
59
78
96
91
87
83
79
75
71
67
63
60
80
96
92
87
83
79
75
72
68
64
61
82
96
92
88
84
80
76
72
69
65
62
84
96
92
88
84
80
77
73
69
66
63
86
96
92
88
84
81
77
73
70
67
63
88
96
92
88
85
81
77
74
71
67
64
90
96
92
88
85
81
78
74
71
68
65
The table may be readily understood. For example, if the temperature of the
air (dry bulb) be 60, and the temperature of evaporation (wet bulb) be 56, the
difference being 4, look in the column headed " Temperature of the air 7 for 60,
and for the figures on the same line in column headed 4; here 78 wiU be found,
which means that the air is 78 per cent saturated with water vapor; that is, that the
amount of water vapor present in the atmosphere is 78 per cent of the total amount
that it could carry at the given temperature (60). This total amount, or saturation,
is thus represented by 100, and if there occurred any increase of the quantity ^of
vapor beyond this point, the excess would be precipitated in the form of liquid.
Over the ocean s surface the relative humidity is generally about 90 per cent, or even
higher in the doldrums; over the land in dry winter weather it may fall as low as
40 per cent.
64. The sea water of which the temperature is to be taken should be drawn from
a depth of 3 feet below the surface, the bucket used being weighted in order to sink
it. The bulb of the thermometer should remain immersed in the water at least
three minutes before reading, and the reading should be made with the bulb
immersed.
INSTRUMENTS AND ACCESSORIES IN NAVIGATION. 31
THE LOG BOOK.
65. The Log Book is a record of the ship s cruise, and, as such, an important
accessory in the navigation. It should afford all the data from which the position
of the snip is established by the method of dead reckoning; it should also comprise
a record of meteorological observations, which should be made not only for the purpose
of foretelling the weather during the voyage, but also for contribution to the general
fund of knowledge of marine meteorology.
66. A convenient form for recording the data, which is employed for the log
books of United States naval vessels, is shown on page 32 ; beside the tabulated matter
thus arranged, to which one page of the book is devoted, a narrative of the miscella
neous events of the day, written and signed by the proper officers, appears upon the
opposite page.
32
INSTRUMENTS AND ACCESSORIES IN NAVIGATION.
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INSTRUMENTS AND ACCESSORIES IN NAVIGATION.
33
67. For the most part, the nature of the information called for, with the method
of recording it, will be apparent. A brief explanation is here given of such points
as seem to require it.
68. THE WIND. In recording the force of the wind the scale devised by the
late Admiral Sir F. Beaufort is employed. According to this scale the wind varies
from 0, a calm, to 12, a hurricane, the greatest velocity it ever attains. In the lower
grades of the scale the force of the wind is estimated from the speed imparted to a
man-of-war of the early part of the nineteenth century sailing full and by; in the
higher grades, from the amount of sail which the same vessel could carry when
close-hauled. The scale, with the estimated velocity of the wind in both statute and
nautical miles per hour, is as follows :
Force of -wind.
Conditions.
Velocity.
Mean pressure
in pounds
per square
foot.
Statute miles per Nautical miles per
hour. hour.
Calm
Full-rigged ship, all sails set, no headway. .
Just sufficient to give steerage wav
to 3
8
13
18
23
28
34
40
48
56
65
75
90 and over.
to 2.G
6.9
11.3
15.6
20.0
24.3
29.5
34.7
41.6
48.6
56.4
65.1
78. 1 and over.
O.C3
0.23
0.62
1.2
1.9
2.9
4.2
5.9
S.4
11.5
15.5
20.6
29.6
1 Light air
2 Light breeze
Speed of 1 or 2 knots, " full and by "
3 Gentle breeze
Speed of 3 or 4 knots, "full and by"...
4. Moderate breeze . . .
5 Fresh breeze
Speed of 5 or 6 knots, "full and by "
All plain sail "full and by "..
6 Strong breeze
7. Moderate gale
8. Fresh gale
T opgallant sails over single-reefed topsails. .
Double-reefed topsails
Treble-reefed topsails (or reefed upper
topsails and courses).
Close-reefed topsails and courses (or lower
topsails and courses).
Close-reefed main topsail and reefed fore
sail (or lower main topsail and reefed
foresail).
Storm staysails
9. Strong gale
10 Whole gale
11. Storm
12. Hurricane
Under bare poles
69. When steaming or sailing with any considerable speed, the apparent direc
tion and force of the wind, as determined from a vane flag, or pennant aboard ship,
may differ materially from the true direction and force, the reason being that the
air appears to come from a direction and with a force dependent, not only upon the
wind itself, but also upon the motion of the vessel. For instance, suppose that the
wind has a velocity of 20 knots an hour (force 4), and take the case 01 two vessels,
eachsteaming 20 knots, the first with the wind dead aft, the second with the wind dead
ahead. The former vessel will be moving with the same velocity as the ah" and in
the same direction; the velocity of the wind relatively to the ship will thus be zero;
on the vessel an apparent calm will prevail and the pennant will hang up and down.
The latter vessel will be moving with the same velocity as the air, but in the opposite
direction; the relative velocity of the two will thus be the sum of the two velocities,
or 40 knots an hour, and on the second vessel the wind will apparently have the
velocity corresponding very nearly with a fresh gale. Again, it might be shown that
in the case of a vessel steaming west at the rate of 20 knots, with the wind blowing
from north with the velocity of 20 knots an hour, the velocity with which the air
strikes the ship as a result of the combined motion will be 23 knots an hour, and the
direction from which it comes will be IN W. If, therefore, the effect of the speed of
the ship is neglected the wind will be recorded as ]S T W., force 6, when in reality it is
north, force 4.
In order to make a proper allowance for this error and arrive at the true direction
and force of the wind, Table 32 may be entered with the ship s speed and the apparent
direction and force of the wind as arguments, and the true direction and force will
be found.
61828 16 3
34 INSTRUMENTS AND ACCESSORIES IN NAVIGATION.
70. WEATHER. To designate the weather a series of symbols devised by the
late Admiral Beaufort is employed. The system employed in the United States Navy
is as follows :
&. Clear blue sky. p. Passing showers of rain.
c. Clouds. 5. Squally weather.
d. Drizzling, or light rain. r. Rainy weather, or continuous rain.
/. Fog, or foggy weather. s. Snow, snowy weather, or snow falling.
f. Gloomy, or dark, stormy-looking weather. t. Thunder.
. Hail. u. Ugly appearances, or threatening weather.
1. Lightning. v. Variable weather.
m Misty weather. w Wet, or heavy dew.
o. Overcast. 2. Hazy weather.
To indicate great intensity of any feature, its symbol may be underlined; thus:
r., heavy rain.
71. CLOUDS. The following are the principal forms of clouds, named in the
order of the altitude above the earth at which they usually occur, beginning with the
most elevated. The symbols by which each is designated follows its name:
1. CIRRUS (Ci.). Detached clouds, delicate and fibrous looking, taking the
form of feathers, generally of a white color, sometimes arranged in belts which cross
a portion of the sky in great circles, and, by an effect of perspective, converging toward
one or two opposite points of the horizon.
2. CIRRO-STRATUS (Ci.-S.). A thin, whitish sheet, sometimes completely cover
ing the sky and only giving it a whitish appearance, or at others presenting, more or
less distinctly, a formation like a tangled web. This sheet often produces halos
around the sun and moon.
3. CIRRO-CUMULUS (Ci.-Cu.). Small globular masses or white flakes, having
no shadows, or only very slight shadows, arranged in groups and often in lines.
4. ALTO-CUMULUS (A.-Cu.). Rather large globular masses, white or grayish,
partially shaded, arranged in groups or lines, and often so closely packed that their
edges appear confused. The detached masses are generally larger and more compact
at the center of the group; at the margin they form into finer flakes. They often
spread themselves out in lines in one or two directions.
5. ALTO-STRATUS (A.-S.). A thick sheet of a gray or bluish color, showing a
brilliant patch in the neighborhood of the sun or moon, and which, without causing
halos, may give rise to coronse. This form goes through all the changes like the
Cirro-Stratus, but its altitude is only half so great.
6. STRATO-CUMULUS (S.-Cu.). Large globular masses or rolls of dark cloud,
frequently covering the whole sky, especially in winter, and occasionally giving it
a wavy appearance. The layer of Strato-Cumulus is not, as a rule, very thick, and
patches of blue sky are often visible through the intervening spaces. All sorts of
transitions between this form and the Alto-Cumulus are noticeable. It may be
distinguished from Nimbus by its globular or rolled appearance and also because it
does not bring rain.
7. NIMBUS (N.). Rain clouds; a thick layer of dark clouds, without shape and
with ragged edges, from which continued rain or snow generally falls. Through the
openings of these clouds an upper layer of Cirro-Stratus or Alto-Stratus may almost
invariably be seen. If the layer of Nimbus separates into shreds or if small loose
clouds are visible floating at a low level underneath a large nimbus, they may be
described as Fracto-Nimbus (Fr.-N.), the "scud" of sailors.
8. CUMULUS (Cu.). Wool-pack clouds; thick clouds of which the upper surface
is dome-shaped and exhibits protuberances, while the base is horizontal. When
these clouds are opposite the sun the surfaces usually presented to the observer have
a greater brilliance than the margins of the protuberances. When the light falls
aslant, they give deep shadows; when, on the contrary, the clouds are on the same
side as the sun, they appear dark, with bright edges. The true Cumulus has clear
superior and inferior limits. It is often broken up by strong winds, and the detached
portions undergo continual changes. These may be distinguished by the name of
Fracto-Cumulus (Fr.-Ou,.).
INSTRUMENTS AND ACCESSORIES IN NAVIGATION. 35
9. CUMULO-NIMBUS (Cu.-N.). The thunder-cloud or shower-cloud; heavy
masses of clouds rising in the form of mountains, turrets, or anvils, generally having
a sheet or screen of fibrous appearance above, and a mass of clouds similar to Nimbus
underneath. From the base there usually fall local showers of rain or of snow
(occasionally hail or soft hail).
10. STRATUS (.). A horizontal sheet of lifted fog; when this sheet is broken
up into irregular shreds by the wind or by the summits of mountains, it may be
distinguished by the name of Fracto-Stratus (Fr.-S.).
72. In the scale for the amount of clouds represents a sky which is cloudless
and 10 a sky which is completely overcast.
73. STATE OF SEA. The state of the sea is expressed by the following system
of symbols :
B. Broken or irregular sea. M. Moderate sea or swell.
C. Chopping, short, or cross sea. R. Rough sea.
G. Ground swell. S. Smooth sea.
H. Heavy sea. T. Tide-rips.
L. Long rolling sea.
NOTE. There are various publications issued by the Hydrographic Office
dealing with special features of navigation, which should be regularly consulted.
Among the most important of these are:
Pilot charts of the various oceans furnish information regarding the drift of
derelicts, ice, and float ing obstructions, the tracks of storms, average conditions of
wind and weather, ocean currents, magnetic variation, etc.
Hydrographic Bulletin, weekly, gives more detailed facts than the Pilot Charts
regarding ice, wrecks, and derelicts; also items on port facilities, use of oil
to calm the sea, and miscellaneous items of use and interest to mariners.
Daily Memorandum, published at the main office at Washington, also makes
public these items through the Branch Hydrographic Offices.
Notice to Mariners, weekly, gives changes in aids to navigation (lights, buoyage,
harbor constructions), dangers to navigation (rocks, shoals, banks, bars), important
new soundings, and, in general, all such facts as affect mariners charts, manuals, and
pilots or sailing directions.
CHAPTER III.
THE COMPASS EEEOE,
CAUSES OF THE ERROR.
74. The properties of magnets are such that when two magnets are near enough
together to exert a mutual influence, those poles which possess like magnetism repel
each other, and those which possess unlike magnetism attract each other.
The earth is a magnetized body, and acts like a great spherical magnet with
poles of unlike magnetism situated within the Arctic and Antarctic circles close to
longitudes 97 west and 155 east of Greenwich, respectively. In common with
magnets, the earth is surrounded by a region in which magnetic influence is exercised
upon the compass, giving the magnetic needle a definite direction in each locality
and causing the end which we name the north pole of the compass to be directed in
general toward the region of the magnetic pole in the geographical north and the
south end toward the region of the magnetic pole in the geographical south.
The north end of the compass north-seeking, as it is sometimes designated for
clearness will be that end which has opposite polarity to the earth s north magnetic
pole, or, otherwise stated, which possesses like magnetism with the earth s south
magnetic pole.
75. By reason of the fact that the magnetic pole in each hemisphere differs in
geographical position by a large and unequal amount from the geographical pole,
we are made aware that the earth is not magnetized symmetrically with reference
to the geographical poles. Hence the directive influence of the earth s magnetism
will not in general cause the compass needle to point in the direction of the true
meridian, but each compass point will differ from the corresponding true point by
an amount varying according to the geographical locality. The angle representing
this difference is the Variation of ike Compass , sometimes also called the Magnetic
Declination. It is the angle between the plane of the true meridian and a vertical
plane passing through a freely suspended magnetic needle influenced solely by the
earth s magnetism.
The variation not only changes as one travels from place to place on the earth,
being different in different localities, but in every locality, besides the minor periodic
movements of the needle known as the diurnal, monthly, and annual variations,
which are not of material concern to the mariner, there is a progressive change
which extends through centuries of time and amounts to large alterations in the
pointing of the compass. ^ In taking account of the effect produced by the variation
of the compass, the navigator must therefore be sure that the variation used is
correct not only for the place, but also for the time under consideration.
Occasionally the magnetic needle is subject to spasmodic fluctuations of the
earth s ^ magnetism lasting from a brief period to several days. These are called
magnetic ^ storms, and are due to sudden changes in the electric currents which cir
culate within the earth and in the region surrounding the earth. They come appar
ently at random, and^ may occur nearly simultaneously over the whole world or be
restricted to a certain region. The range of their effect upon the compass does
not often exceed the half of a degree in the lower latitudes, and hence the navigator
need only be concerned with them in the higher latitudes where he may look to the
aurora as an indication of their occurrence.
76. Besides the error thus produced in the indications of the compass, a further
one, due to Local Attraction, .may arise from extraneous influences due to natural
magnetic attraction in the vicinity of the vessel. Instances of this are quite common
36
THE COMPASS ERROR.
37
when a ship is in port, as she may be in close proximity to vessels, docks, machinery,
or other masses of iron or steel. It is also encountered in the shallow waters of the
sea in localities where the mineral substances in the earth itself possess magnetic
qualities as, for example, at certain places in Lake Superior and at others off the
coast of Australia. When due to the last-named cause, it may be a source of great
danger to the mariner, but, fortunately, the number of localities subject to local
attraction is limited. ^ The amount of this error can seldom be determined except
by survey; if known, it might properly be included with the variation and treated
as a part" thereof.
77. In addition to the variation, the compass ordinarily has a still further
error in its indications, which arises from the effect exerted upon it by masses of
magnetic metal within the shij) itself. This is known as the Deviation of the Compass.
For reasons that will be explained later, it differs in amount for each heading of the
ship, and, further, the character of the deviations undergoes modification as a vessel
proceeds from one geographical locality to another.
APPLYING THE COMPASS ERROR.
78. From what has been explained, it may be seen that there are three methods
by which bearings or courses may be expressed: (a) true, when they refer to the
angular distance from the earth s geographical meridian; (b) magnetic, when they
refer to the angular distance from the earth s magnetic meridian, and must be cor
rected for variation to be converted into true; and (c) by compass, when they refer
to the angular distance from the north indicated by the compass on a given heading
of the ship), and must be corrected for the deviation on that heading for conversion
to magnetic, and for both deviation and variation for conversion to true bearings or
courses. The process of applying the errors under all circumstances is one of which
the navigator must make himself a thorough master; the various problems of con
version are constantly arising; no course can be set nor bearing plotted without
involving the application of this problem, and a mistake in its solution may produce
serious consequences. The student is therefore urged to give it his most careful
attention.
79. When the effect of a compass error, whether arising from variation or from
deviation, is to draw the north end of the compass needle to the right, or eastward,
the error is named east, or is marked + ; when its effect is to draw the north end of
the needle to the left or westward, it is named west, or marked .
Figures 7 and 8 represent, respectively, examples of easterly and westerly errors.
In^botn cases consider that the circles represent the observer s horizon, N and S
being the correct north and south points in each case. If N and S represent the
corresponding points indicated by a compass whose needle is deflected by a compass
error, then in the first case, the north end of the needle being drawn to the right or
east, the error will be easterly or positive, and in the second case, the north end of the
needle being drawn to the left or west, the compass error will be westerly or negative.
38 THE COMPASS ERROR.
Considering figure 7, if we assume the easterly error to amount to one point,
it will be seen that if a direction of N. by W. is indicated by the compass, the correct
direction should be north, or one point farther to the right. If the compass indicates
north, the correct bearing is N. by E.; that is, still one point to the right. If we
follow around the whole card, the same relation will be found in every case, the
corrected bearing being always one point, to the right of the compass bearing.
Conversely, if we regard figure 8, assuming the same amount of westerly error, a
compass bearing of N. by E. is the equivalent of a correct bearing of north, which is
one point to the left; and this rule is general throughout the circle, the corrected
direction being always to the left of that shown by the compass.
80. Having once satisfied himself that the general rule holds, the navigator
may save the necessity of reasoning out in each case the direction in which the error
must be applied, and need only charge his mind with some single formula which will
cover all cases. Such a one is the following:
When the CORRECT direction is to the RIGHT, the error is EAST.
The words correct-right-east, in such a case, would be the key to all of his solutions.
With easterly error, if he had a compass course to change to a corrected one, he
would know that to obtain the result the error must be applied to the right; and,
if it were desired to change a correct course to one indicated by compass, the error
would be applied to the left. If a correct bearing is to be compared with a compass
bearing to find the compass error, when the correct bearing is to the right, the
error is easterly; and when the correct bearing is to the left, the error is westerly.
81. It must be remembered that the word east is equivalent to right in dealing
with the compass error, and west to left, even though they involve an apparent
departure from the usual rules. If a vessel steers NE. by compass with one point
easterly error, her corrected course is NE. by E.; but if she steers SE., the corrected
course is not SE. by E., but SE. by S. Another caution may be necessary to avoid
confusion; the navigator should always regard himself as facing the point under
consideration when he applies an error; one point westerly error on South will bring
a corrected direction to S. by E.; but if we applied one point to the left of South
while looking at the compass card in the usual way north end up S. by W. would
be the point arrived at, and a mistake of two points would be the result.
82. In the foregoing explanation reference has been made to i correct " directions
and "compass errors without specifying "magnetic" and "true" or "variation"
and "deviation." This has been done in order to make the statements apply to all
cases and to enable the student to grasp the subject in its general bearing without
confusion of details.
Actually, as has already been pointed out, directions given may be true, magnetic,
or by compass. By applying variation to a magnetic bearing we correct it and make
it true, by applying a deviation to a compass bearing we correct it to magnetic, and
by applying to it the combined deviation and variation we correct it to true. Which
ever of these operations is undertaken, and whichever of the errors is considered, the
process of correction remains the same; the correct direction is always to the right,
when the error is east, by the amount of that error.
Careful study of the following examples will aid in making the subject clear:
EXAMPLES: A bearing taken by a compass free from deviation is 76; variation,
5 W.; required the true bearing. 71.
A bearing taken by a similar compass is NW. by W. J W.; variation, J pt. W.;
required the true bearing. NW. by W. f W.
A vessel steers 153 by compass; deviation on that heading, 3 W.; variation
in the locality, 12 E.; required the true course. 162.
A vessel steers S. by W. JW.: deviation, \ pt. W.; variation, 1 pt, E.: required
the true course. SSW. J W.
It is desired to steer the magnetic course 322; deviation, 4 E.; required the
course by compass. 318.
The true course between two points is found to be W. } N.; variation, 1J pt.
E.; no deviation; required the compass course. W. f S.
True course to be made, 55; deviation, 7 E.; variation, 14 W.; required the
course by compass. 62.
THE COMPASS ERROR. 39
A vessel passing a range whose direction is known to be 200, magnetic, observes
the bearing by compass to be 178; required the deviation. 22 E.
The sun s observed bearing by compass is 91; it is found by calculation to be
84 (true); variation, 8 W.; required the deviation. 1 E.
FINDING THE COMPASS ERROR.
83. The variation of the compass for any given locality is found from the
charts. A nautical chart always contains information from which the navigator is
enabled to ascertain the variation for any place within the region embraced and
for any year. Beside the information thus to be acquired from local charts, special
charts are published showing the variation at all points on the earth s surface.
84. The deviation of the compass, varying as it does for every ship, for every
heading, and for every geographical locality, must be determined by the navigator,
for which purpose various methods are available.
Whatever method is used, the ship must be swung in azimuth and an observa
tion made on each of the headings upon which the deviation is required to be known.
If a new iron or steel ship is being swung for the first time, observations should be
made on each of the twenty-four 15 rhumbs into which the compass card is divided.
At later swings, especially after correctors have been applied, or in the case of wooden
ships, twelve 15 rhumbs wiU suffice or, indeed, only six. In case it is not prac
ticable to make observations on exact 15 rhumbs, they should be made as near
thereto as practicable and plotted on the Napier diagram (to be explained hereafter),
whence the deviations on exact 15 rhumbs may be found.
85. In swinging ship for deviations the vessel should be on an even keel and all
movable masses of iron in the vicinity of the compass secured as for sea, and the com
pass accurately centered in the binnacle. The vessel, upon being placed on any head
ing, should be steadied there for three or four minutes before the observation is made,
in order that the compass card may come to rest and the magnetic conditions assume
a settled state. To assure the greatest accuracy the ship should first be swung to
starboard, then to port, and the mean of the two deviations on each course taken.
Ships may be swung under their own steam, or with the assistance of a tug, or at
ancnor, where the action of the tide tends to turn them in azimuth (though in this
case it is difficult to get them steadied for the requisite time on each heading), or at
anchor, by means of springs and hawsers.
86. The deviation of all compasses on the ship may be obtained from the same
swing, it being required to make observations with me standard only. To accomplish
this it is necessary to record the ship s head by all compasses at the time of steadying
on each even rhumb of the standard; applying the deviation, as ascertained, to the
heading by standard, gives the magnetic heads, with which the direction of the ship s
head by each other compass may be compared, and the deviation thus obtained.
Then a complete table of deviations may be constructed as explained in article 94.
87. There are four methods for ascertaining the deviations from swinging;
namely, by reciprocal bearings, by bearings of the sun, by ranges, and by a distant
object"
88. RECIPROCAL BEARINGS. One observer is stationed on shore with a spare
compass placed in a position free from disturbing magnetic influences; a second
observer is at the standard compass on board ship. At the instant when ready for
observation a signal is made, and each notes the bearing of the other. The bearing
by the shore compass, reversed, is the magnetic bearing of the shore station from the
ship, and the difference between this and the bearing by the ship s standard compass
represents the deviation of the latter.
In determining the deviations of compasses placed 011 the fore-and-aft amidship
line, when the distribution of magnetic metal to starboard and port is symmetrical,
the shore compass may be replaced by a dumb compass, or pelorus, or by a theodolite
in which, for convenience, the zero of the horizontal graduated circle may be termed
north; the reading of the shore instrument will, of course, not represent magnetic
directions, but by assuming that they do we obtain a series of fictitious deviations,
the mean value of which is the error common to all. Upon deducting this error
from each of the fictitious deviations, we obtain the correct values.
40 THE COMPASS ERROR.
If ship and shore observers are provided with watches which have been com
pared with one another, the times may be noted at^ each observation, and thus
afford a means of locating errors due to misunderstanding of signals.
89. BEARINGS OF THE SUN. In this method it is required that on each heading
a bearing of the sun be observed by compass and the time noted at the same moment
by a chronometer or watch. By means which will be explained in Chapter XIV, the
true bearing of the sun may be ascertained from the known data, and this, compared
with the compass bearing, gives the total compass error; deducting from the compass
error the variation, there remains the deviation. The variation used may be that
given by the chart, or, in the case of a compass affected only by symmetrically placed
iron or steel, may be considered equal to the mean of all the total errors. Other
celestial bodies may be observed for this purpose in the same manner as the sun.
This method is important as being the most convenient one available for deter
mining the compass error at sea. When adjusting compasses much time will be
saved by this simple modification of a detail:
Instead of tabulating magnetic azimuths for given stated times in advance, draw
on cross-section paper a curve whose ordinates are minutes of local apparent time and
whose abscissae are degrees of magnetic azimuth, that is, true azimuth corrected for
variation. Then for any given instant (the navigator s watch being set to local
apparent time) the magnetic azimuth may be read directly from the curve. The
difference between the magnetic azimuth of the sun and its compass bearing is, of
course, the deviation of the compass on that particular heading.
90. RANGES. In many localities there are to be found natural or artificial
range marks which are clearly distinguishable, and which when in line lie on a known
magnetic bearing. By steaming about on different headings and noting the compass
bearing of the ranges each time of crossing the line that they mark, a series of devia
tions may be obtained, the deviation of each heading being equal to the difference
between the compass and the magnetic bearing.
91. DISTANT OBJECT. A conspicuous object is selected which must be at a con
siderable distance from the ship and upon which there should be some clearly defined
point for taking bearings. The direction of this object by compass is observed on
successive headings. Its true or magnetic bearing is then found and compared with
the compass bearings, whence the deviation is obtained.
The true or the magnetic bearing may be taken from the chart. The magnetic
bearing may also be found by setting up a compass ashore, free from foreign magnetic
disturbance, in range with the object and the ship, and observing the bearing of the
object; or the magnetic bearing may be assumed to be the mean of the compass
bearings.
In choosing an object for use in this method care must be taken that it is at such
a distance that its bearing from the ship does not practically differ as the vessel
swings in azimuth. If the ship is swung at anchor, the distance should be not less
than 6 miles. If swung under way, the object must be so far that the parallax
(the tangent of which may be considered equal to half the diameter of swinging
divided by the distance) shall not exceed about 30 .
92. In all of the methods described it will be found convenient to arrange the
results in tabular form. In one column record the ship s head by standard compass,
and abreast it in successive columns the observations from which the deviation is
determined on that heading, and finally write the deviation itself. When tha result
of the swing has been worked up, another table is constructed showing simply the
headings and the corresponding deviations. This is known as the Deviation Table
of the^compass. If compensation is to be attempted, this table is the basis of the
operation; if not, the deviation tables of the standard and steering compass should
be posted in such place as to be accessible to all persons concerned with the naviga
tion of the ship.
THE COMPASS ERROR.
41
93. Let it be assumed that a deviation table has been found ancl that the values
are as follows:
Deviation table.
Ship s head by standard compass
Deviation.
Ship s head by standard compass.
Deviation.
North
-15 29
South
180
+ 17 5
Bra
15
30
45
-14 53
-13 16
11 19
SW
195
210
225
+23 47
+27 07
+ 9 5 35
Ea^t
60
75
90
- 9 59
- 9 42
- 9 06
West
240
255
270
+21 57
+15 54
+ 9 56
SE
105
120
135
- 9 01
- 7 51
- 5 54
xw
285
300
.315
+ 1 56
- 4 09
-10 20
150
165
- 2 16
+ 8 29
330
345
-13 37
-16 01
We have from the table the amount of deviation on each compass heading;
therefore, knowing the ship s head by compass, it is easy to pick out the corresponding
deviation and thus to obtain the magnetic neading. But if we are given the magnetic
direction in which it is desired to steer and have to find the corresponding compass
course, the problem is not so simple, for we are not given deviations on magnetic
heads, and where the errors are large it may not be assumed that they are the same
as on the corresponding compass headings. For example, with the deviation table
just given, suppose it is required to determine the compass heading corresponding
to 165, magnetic.
The deviation corresponding to 165, per compass, is + 84-. If we apply this
to 165, magnetic, we have 156 as the compass course. But, consulting the table,
it may be seen that the deviation corresponding to 156^, per compass, is + 2J, and
therefore if we steer that course the magnetic direction will be 159, and not 165,
as desired.
A way of arriving at the correct result is to make a series of trials until a course
is arrived at which fulfills the conditions. Thus, in the example given:
First trial.
Mag. course desired ...................... 165
Try dev. on 165 ....................... 8i E.
Trial comp. course
Dev. o
E.
Mag. course made good .................. 159
Since this assumption carries the course 6 too far
to the left, assume next a deviation on a course 3^
farther to the right than the one used here.
Second trial.
.Mag. course desired 165
Trvdev. on 160... 5 E.
Trial comp. course 160 C
Dev. on 160 5 C
Mag. course made good 165
This happens to be exactly the compass course
required. But it often occurs that further trials
may be necessary.
94. THE NAPIER DIAGRAM. A much more expeditious method for the solution
of this problem is afforded by the Napier Diagram, and as that diagram also facilitates
a number of other operations connected with compass work it should be clearly
understood by the navigator. This admits of a graphic representation of the table
of deviations of the compass by means of a curve; besides furnishing a ready means
of converting compass into magnetic courses and the reverse, one of its chief
merits is that if the deviation has been determined on a certain number of head
ings it enables one to obtain the most probable value of the deviation on any
other course that the ship may head. The last-named feature renders it useful in
making a table of deviations of compasses other than the standard when their errors
are found as described in article 86.
95. The Napier diagram (fig. 9) represents the margin of a compass card cut
at the north point and straightened into a vertical line; for convenience, it is usually
divided into two sections, representing, respectively, the eastern and western semi
circles. The vertical line is of a convenient length and divided into twenty-four
equal parts corresponding to the 15 rhumbs of the compass, beginning at the top
42
THE COMPASS ERROR.
with North and continuing around to the right; it is also divided into 360 degrees,
which are appropriately marked.
To obtain a complete curve, a sufficient number of observations should be taken
while the ship swings through an entire circle. Generally, observations on every
alternate 15 rhumb are enough to establish a good curve, but in cases where the
maximum deviation reaches 40 it is preferable to observe on every 15 rhumb.
Compass courses on dotted tines.
Magnetic courses on solid linos.
FROM NORTH TO 180 SOUTH
DEVIATION DEVIATION
WEST NORTH EAST
FROM 180 SOUTH TO 360 NORTH
DEVIATION DEVIATION
WEST SOOTH EAST
of Total Deviation
of Semicircular Component
of Quadrjjm-tal Component
FIG. 9.
The curve shown in the full line on figure 9 corresponds to the table of deviations
given in article 93.
From a given^ compass course to find the corresponding magnetic course, through the
point of the vertical fine representing the given compass course draw a line parallel
to the dotted lines until the curve is intersected, and from the point of intersection
draw another line parallel to the plain lines; the point on the scale where this last
THE COMPASS ERROR.
43
line cuts the vertical line is the magnetic course sought. The correctness of this
solution will be apparent when we consider that the 60 triangles are equilateral, and
therefore the distance measured along the vertical side will equal the distance meas
ured along the inclined sides that is, the deviation; and the direction will be correct,
for the construction is such that magnetic directions will be to the right of compass
directions when the deviation is easterly and to the left if westerly.
From a given magnetic course to find the corresponding compass course, the process
is the same, excepting that the first line drawn should follow, or be parallel to, the
plain lines, and the second, or return line, should be parallel to the dotted; and a
proof similar to that previously employed will show the correctness of the result.
As an example, the problem given in article 93 may be solved by the diagram, and
the result will be found to accord with the solution previously given.
The vertical line is intersected at each 15 rhumb by two lines inclined to it at
an angle of 60, that line which is inclined upward to the right being drawn plain
and the other dotted.
To plot a curve on the Napier diagram, if the deviation has been observed with
the ship s head on given compass courses (as is usually the case with the standard
compass), measure off on the vertical scale the number of degrees corresponding to
the deviation and lay it down to the right if easterly and to the left if westerly
on the dotted line passing through the point representing the ship s head; or, if the
observation was not made on an even 15 rhumb, then lay it down on a line drawn
parallel to the dotted ones through that division of the vertical line which represents
the compass heading; if the deviation has been observed with the ship on given
magnetic courses (as when deviations by steering compass are obtained by noting
the ship s head during a swing on even 15 rhumbs of the standard), proceed in the
same way, excepting that the deviation must be laid down on a plain line or a line
parallel thereto. Mark each point thus obtained with a dot or small circle, and draw
a free curve passing, as nearly as possible, through all the points.
THE THEORY OF DEVIATION."
96. FEATURES OF THE EARTH S MAGNETISM. It has already been stated that
the earth acts like a great spherical magnet, with a pole in each hemisphere which is
not coincident with the geographical pole; it has
also a magnetic equator which lies close to, but
not coincident with, the geographical equator.
A magnetic needle freely suspended at a
point on the earth s surface, and undisturbed by
any other than the earth s magnetic influence,
will lie in the plane of the magnetic meridian
and at an angle with the horizon depending upon
the geographical position.
The magnetic elements of the earth which
must be considered are shown in figure 10.
The earth s total force is represented in direction
and intensity by the line AB. Since compass
needles are mechanical! v arranged to move only
in a horizontal plane, it Tbecomes necessary, when
investigating the effect of the earth s magnetism
upon them, to resolve the total force into two
components which in the figure are represented
by AC and AD. These are known, respectively,
as the horizontal and vertical components of the
earth s total force, and are usually designated as
H and Z. The angle CAB, which the line of direction makes with the plane of
the horizon, is called the magnetic inclination or dip, and denoted by 0.
It is clear that the horizontal component will reduce to zero at the magnetic
poles, where the needle points directly downward, and that it will reach a maximum
a As it is probable that the student will not have practical need of a knowledge of the theory of deviation and the compensation
of the compass until after he has mastered all other subjects pertaining to Navigation and Nautical Astronomy, it may be considered
preferable to omit the remainder of this chapter at first and return to it later.
FIG. 10.
44 THE COMPASS ERROR.
at the magnetic equator, where the free needle hangs in a horizontal direction. The
reverse is true of the vertical component and of the angle of dip.
Values representing these different terms may be found from special charts.
97. INDUCTION; HARD AND SOFT IRON. -When a piece of unmagnetized iron
or steel is brought within the influence of a magnet, certain magnetic properties are
immediately imparted to the former, which itself becomes magnetic and continues to
remain so as long as it is within the sphere of influence of the permanent magnet;
the magnetism that it acquires under these circumstances is saia to be induced, and
the properties of induction are such that that end or region which is nearest the pole
of the influencing magnet will take up a polarity opposite thereto. If the magnet is
withdrawn, the induced magnetism is soon dissipated. If the magnet is brought into
proximity again, but with its opposite pole nearer, magnetism will again be induced,
but this time its polarity will be reversed. A further property is that if a piece of iron
or steel, while temporarily possessed of magnetic qualities through induction, be
subjected to blows, twisting, or mechanical violence of any sort, the magnetism is
thus made to acquire a permanent nature.
The softer the metal, from a physical point of view, the more quickly and thor
oughly will induced magnetism be dissipated when the source of influence is with
drawn; hard metal, on the contrary, is slow to lose the effect of magnetism imparted
to it in any way. Hence, in regarding the different features which affect deviation,
it is usual to denominate as hard iron that which possesses retained magnetism of a
stable nature, and as soft iron that which rapidly acquires and parts with its mag
netic qualities under the varying influences to which it is subjected.
98. MAGNETIC PROPERTIES ACQUIRED BY AN IRON OR STEEL VESSEL IN
BUILDING. The inductive action of the earth s magnetism affects all iron or steel
within its influence, and the amount and permanency of the magnetism so induced
depends upon thd position of the metal with reference to tha earth s total force,
upon its character, and upon the degree of hammering, bending, and twisting that it
undergoes.
An iron bar held in the line of the earth s total force instantly becomes magnetic;
if held at an angle thereto it would acquire magnetic properties dependent for their
amount upon its inclination to the line of total force; when held at right angles to
the line there would be no effect, as each extremity would be equally near the proles
of the earth and all influence would be neutralized. If, while such a bar is in a
magnetic state through inductive action, it should be hammered or twisted, a certain
magnetism of a permanent character is impressed upon it, which is never entirely
lost unless the bar is subjected to causes equal and opposite to those that produced
the first effect.
A sheet of iron is affected by induction in a similar way, the magnetism induced
by the earth diffusing itself over the entire plate and separating itself into regions
of opposite polarity divided by a neutral area at right angles to the earth s line of
total force. If the plate is hammered or bent, this magnetism takes up a permanent
character.
^ If the magnetic mass has a third dimension, and assumes the form of a ship, a
similar condition prevails. The whole takes up a magnetic character; there is a
magnetic axis in the direction of the line of total force, with poles at its extremities
and a zone of no magnetism perpendicular to it. The distribution of magnetism
will depend upon the horizontal and vertical components of the earth s force in the
locality and upon the direction of the keel in building; its permanency will depend
upon the amount of mechanical violence to which the metal has been subjected by
the riveting and other incidents of construction, and upon the nature of the metal
employed.
99. CAUSES THAT PRODUCE DEVIATION. There are three influences that
operate to produce deviation; namely, (a) subpermanent magnetism; (b) transient
magnetism induced in vertical soft iron, and (c) transient magnetism induced in hori
zontal soft iron. Their effect will be explained.
Subpermanent magnetism is the name given to that magnetic force which origi
nates in the ship while building, through the process explained in the preceding
article; after the vessel is launched and has an opportunity to swing in azimuth,
the magnetism thus induced will suffer material diminution until, after the lapse of
THE COMPASS ERROR. 45
a certain time, it will settle down to a condition that continues practically unchanged;
the magnetism that remains is denominated subpermanent. The vessel will then
approximate to a permanent magnet, in which the north polarity will lie in that
region which was north in building and the south polarity (that which exerts an
attracting influence on the north pole of the compass needle) in the region which
was south in building.
Transient magnetism induced in vertical soft iron is that developed in the soft
iron of a vessel through the inductive action of the vertical component only of the
earth s total force, and is transient in nature. Its value or force in any given mass
varies with and depends upon the value of the vertical component at the place,
and is proportional to the sine of the dip, being a maximum at the magnetic pole
and zero at the magnetic equator.
Transient magnetism induced in horizontal soft iron is that developed in the soft
iron of a vessel through the inductive action of the horizontal component only of
the earth s total force, and is transient in nature. Its value or force in any given
mass varies with and depends upon the value of the horizontal component at the
place, and is proportional to the cosine of the dip, being a maximum at the magnetic
equator and reducing to zero at the magnetic pole.
The needle of a compass in any position on board ship will therefore be acted
upon by the earth s total force, together with the three forces just described. The
poles of these forces do not usually lie in the horizontal plane of the compass needle,
but as this needle is constrained to act in a horizontal plane, its movements will be
affected solely by the horizontal components of these forces, and its direction will
be determined by the resultant of those components.
The earth s force operates to retain the compass needle in the plane of the
magnetic meridian, but the resultant of the three remaining forces, wnen without
this plane, deflects the needle, and the amount of such deflection constitutes the
deviation.
100. CLASSES OF DEVIATION. Investigation has developed the fact that the
deviation produced as described is made up of three parts, which are known respec
tively as Semicircular, quadrantal, and constant deviation, the latter being the least
important. A clear understanding of the nature of each of these classes is essential
for a comprehension of the methods of compensation.
101. Semicircular Deviation is that due to the combined influence, exerted in a
horizontal plane, of the subpermanent magnetism of a ship and of the magnetism
induced in soft iron by the vertical component of the earth s force. If we regard the
effect of these two forces as concentrated in a single resultant pole exerting an
attracting influence upon the north end of the compass needle, it may be seen that
there will be some heading of the ship whereon that pole will lie due north of the
needle and therefore produce no deviation; now consider that, from this position,
the ship s head swings in azimuth to the right; throughout all of the semicircle first
described an easterly deviation will be produced, and, after completing 180, the pole
will be in a position diameterically opposite to that from which it started, and will
again exert no influence that tends to produce deviation. Continuing the swing,
throughout the next semicircle the direction of the deviation produced will be always
to the westward, until the circle is completed and the ship returns to her original
neutral position. From the fact that this disturbing cause acts in the two semicircles
with equal and opposite effect it is given the name of semicircular deviation.
In figure 9 a curve is depicted winch shows the deviations of a semicircular nature
separated from those due to other disturbing causes, and from this the reason for
the name will be apparent.
102. Returning to the two distinct sources from which the semicircular deviation
arises, it may be seen that the force due to subpermanent magnetism remains constant
regardless of the geographical position of the vessel; but since the horizontal force
of the earth, which tends to hold the needle in the magnetic meridian, varies with the
magnetic latitude, the deviation due to subpermanent magnetism varies inversely as
the horizontal force, or as Y>; this may be readily understood if it is considered that
the stronger the tendency to cling to the direction of the magnetic meridian the less
will be the deflection due to a given disturbing force. On the other hand, that part
46
THE COMPASS ERROR.
of the semicircular force due to magnetism induced in vertical soft iron varies as the
earth s vertical force, which is proportional to the sine of the dip; its effect in producing
deviation, as in the preceding case, varies inversely as the earth s horizontal force
that is, inversely as the cosine of the dip ; hence the ratio representing the change of
sin
deviation arising from this cause on change of latitude is - ^, or tan 6.
C/OS (7
If, then, we consider the change in the semicircular deviation due to a change
of magnetic latitude, it will be necessary to separate the two factors of the deviation
and to remember that the portion produced by subpermanent magnetism varies as
TJ, and that due to vertical induction as tan 6. But for any consideration of the
effect of this class of deviation in one latitude only, the two parts may be joined
together an d regarded as having a single resultant.
103. Assuming that all the forces tending to produce semicircular deviation
are concentrated in a single pole exerting an influence on the north pole of the
compass, it will be seen that this can be resolved into a horizontal and a vertical
component, just as the earth s magnetic force is illustrated in figure 10. It is now
evident, therefore, that the horizontal component of this
single magnet may be resolved into two components one
fore-and-aft, and one athwartship; in this case, the semi-
> circular forces will be represented by two magnets, one fore-
/ and-aft and the other athwartship, and compensation may
/ be made by two separate magnets lying respectively in the
directions stated, but with their north or repelling poles in
the position occupied by the south or attracting poles of the
ship s force.
Figure 11 represents the conditions that have been
described. Let O be the center of the compass, XX 7 and
YY , respectively, the fore-and-aft and athwartship lines of
the ship, and OS the direction in which the attracting pole of
the disturbing force is exerted. Now, if OP be laid off on
the line OS, representing the amount of the disturbing force
according to some convenient scale, then O& and Oc, respec
tively, represent, on the same scale, the resolved directions of
that force in the keel line and in the transverse line of the
ship. Each of these resolved forces will exert a maximum
effect when acting at right angles to the needle, the athwart
ship one when the ship heads north or south by compass,
and the longitudinal one when the heading is east or west.
On any other heading than those named the deviation pro
duced by each force will be a fraction of its maximum whose
magnitude will depend upon the azimuth of the ship s head. The maximum devia
tion produced, therefore, forms in each case a basis for reckoning all of the various
effects of the disturbing force, and is called a coefficient.
The coefficient of semicircular deviation produced by the force in the fore-and-aft
line is called B, and is reckoned as positive when it attracts a north pole toward the
bow , negative when toward the stern; that produced by the athwartship force is C,
and is reckoned as positive to starboard and negative to port. These coefficients are
expressed in degrees. a
104. The coefficient B is approximately equal to the deviation on East; or to
the deviation on West with reversed sign; or to the mean of these two. Thus in
the ship having the table of deviations previously given (art. 93), B is equal to
-9 06 , or to -9 56;, or to (-9 06 -9 56 ) = -9 31 .
^The coefficient C is approximately equal to the deviation on North; or to the
deviation on South with reversed sign; or to the mean of these two. In the example
C is equal to -15 29 , or to -17 52 , or to i (-15 29 -17 52 )= -16 40 .
o It should be remarked that in a mathematical analysis of the deviations, it would be necessary to distinguish between the
approximate coefficients, B and C, here described, as alsa A, D, and E, to be mentioned later, and the exact coefficients denoted by
the corresponding capital letters of the German alphabet, which latter are in reality the forces producing those deviations expressed
in terms of the "mean force to north" (An), as unit. In the practical discussion of the subject here given, the question of the dif
ference need not be entered into further.
FIG. 11.
THE COMPASS ERROR.
47
105. The value of the subpermanent magnetism remaining practically constant
under all conditions, it will not alter when the ship changes her latitude; but that
due to induction in vertical soft iron undergoes a change when, by change of geo
graphical position, the vertical component of the earth s force assumes a different
value, and in such case the correction by means of one or a pair of permanent magnets
will not remain effective. If, however, by series of observations in two magnetic
latitudes, the values of the coefficients can be determined under the differing cir
cumstances, it is possible, by solving equations, to determine what effect each force
has in producing the semicircular deviation; having done which, the subpermanent
magnetism can be corrected by permanent magnets after the method previously
described, and the vertical induction in soft iron can be corrected by a piece of
vertical soft iron placed in such a position near the compass as to produce an equal
but opposite force to the ship s vertical soft iron. This last corrector is called a
Flinders par.
Having thus opposed to each of the component forces a corrector of magnetic
character identical with its own, a change of latitude will make no difference in the
effectiveness of the compensation, for in every case the modified conditions will
produce identical results in the disturbing and in the correcting force.
106. Quadrantal Deviation is that which arises from horizontal induction in the
soft iron of the vessel through the action of the horizontal component of the earth s
total force. Let us consider, in figure 12, the effect of any piece of soft iron which
is symmetrical with respect to the compass that
is, which lies wholly within a plane passing through
the center of the needle in either a fore-and-aft or
an athwartship direction. It may be seen (a) that
such iron produces no deviation on the cardinal
points (for on north and south headings the fore-
and-aft iron, though strongly magnetized, has no
tendency to draw the needle from a north-and-south
line, while the athwartship iron, being at right angles
to the meridian, receives no magnetic induction,
and therefore exerts no force; and on east and
west headings similar conditions prevail, the athwart
ship and the fore-and-aft iron having simply ex
changed positions) ; and (&) the direction of the
deviation produced is opposite in successive quad
rants. The action of unsyinmetrical soft iron is
FIG. 12.
not quite so readily apparent, but investigation shows that part of its effect is to
produce a deviation which becomes zero at the inter-cardinal points and is of oppo
site name in successive quadrants. From the fact that deviations of this class
change sign every 90 throughout the circle, they gain the name of quadrantal devi
ations. One of the curves laid down in the Napier diagram (fig. 9) is that of quad-
rantal deviations, whence the nature of this disturbance of the needle may be
observed.
107. All deviations produced by soft iron may be considered as fractions of
the maximum deviation due to that disturbing influence; and consequently the
maximum is regarded as a coefficient, as in the case of semicircular deviations.
The coefficient due to symmetrical soft iron is designated as D, and is considered
positive when it produces easterly deviations in the quadrant between North and
East; the coefficient of deviations arising from unsymmetrical soft iron is called E,
and is reckoned as positive when it produces easterly deviations in the quadrant
between ^NW. and NE.; this latter attains importance only when there is some
marked inequality in the distribution of metal to starboard and to port, as in the
case of a compass placed off the amidship line.
108. D is approximately equal to the mean of the deviations on NE. and SW.;
or to the mean of those on SE. and NW., with sign reversed; or to the mean of those
means. In the table of deviations given in article 93, D is equal to ^ ( 11 19 / + 25
35 ) =+ 7 08 , or to ( + 5 54 + 10 20 ) = +8 07 ; or to J (708 / + 807 / ) = + 737 .
By reason of the nature of the arrangement of iron in a ship, D is almost invariably
positive.
48 THE COMPASS ERBOK.
E is approximately equal to the mean of the deviations on North and South; or
to the mean of those on East and West with sign reversed; or to the mean of those
means. In the example, E is equal to ^ (-15 29 / + 17 52 )= +1 11 ; or to
i ( + 9 06 -9 56 )=-025 ; or to J ( + 1 ll -0 25 ) = +0 23 .
109. Quadrantal deviation does not, like semicircular, undergo a change upon
change of magnetic latitude ; being due to induction in horizontal soft iron, the magnetic
force exerted to produce it is proportional to the horizontal component of the earth s
magnetism; but the directive force of the needle likewise depends upon that same
component ; consequently, as the disturbing force exerted upon the needle increases,
so does the power that holds it in the magnetic ^meridian," with the result that on
any given heading the deflection due to soft iron is always the same.
110. Quadrantal deviation is corrected by placing masses of soft iron (usually
two hollow spheres in the athwartship line, at equal distances on each side of the
compass) , with the center of mass in the horizontal plane of the needle. The distance
is made such that the force exerted exactly counteracts that of the ship s iron. As
the correcting effect of this iron will, like the directive force and the quadrantal
disturbing force, vary directly with the earth s horizontal component, the compen
sation once properly made will be effective in all latitudes; provided that the compass
needles are short and, consequently, exercise little or no induction on the quadrantal
correctors.
With compasses such as the United States Navy standard 7 J-inch liquid compass,
the needles of which are long and powerful, it will usually be found that the position
of the spheres must be changed with change of latitude. This may be accounted for
by the magnetism induced in the spheres by the compass needles at the same time
and in the same manner as the earth s force. In this case the quadrantal correcting
force is the resultant of the constant force due to the induction of the needles in the
spheres and the variable force (the earth s horizontal force, H, varying with change
in magnetic latitude) due to the induction of the earth in the spheres. This resultant
of these two forces is a variable force, and, after a given quadrantal deviation is
corrected in one latitude by this force, the balance will be changed upon going into
another latitude and the correction will fail to hold good.
In practice, the quadrantal deviation due to unsymmetrical iron is seldom
corrected; the correction may be accomplished, however, by placing the soft iron
masses on a line which makes an angle to the athwartship line through the center
of the card.
111. Constant Deviation is due to induction in horizontal soft iron unsym-
metrically placed about the compass. It has already been explained that one effect
of such iron is to produce a quadrantal deviation, represented by one coefficient E ;
another effect is the constant deviation, so called because it is uniform in amount
and direction on every heading of the ship. If plotted on a Napier diagram, it would
appear as a straight line parallel with the initial line of the diagram.
112. Like other classes of deviation, the effect of the disturbing force is repre
sented by a coefficient ; this coefficient is designated as A, and is considered plus for
easterly and minus for westerly errors. It is approximately equal to the mean of
the deviations on any number of equidistant headings. In the case previously given,
it might be found from the four headings, North, East, South, and West, and would
then be equal to J (-15 29 -9 06 + 17 52 + 9 50 )= +0 48 ; or from all of
the 24 headings, when it would equal 01 .
For the same reason as in the case of E, the value of A is usually so small that
it may be neglected; it only attains a material size when the compass is placed off
the midship line, or for some similar cause.
113. Like quadrantal deviation, since its force varies with the earth s horizontal
force, the constant deviation will remain uniform in amount in all latitudes. (See
art. 110.)
No attempt is made to compensate for this class of error.
114. COEFFICIENTS. The chief value of coefficients is in mathematical analyses
of the deviations and their causes. It may, however, be a convenience to the practical
navigator to find their approximate values by the methods that have been given, in
order that he may gain an idea of the various sources of the error, with a view to
ameliorating the conditions, when necessary, by moving the binnacle or altering the
THE COMPASS ERROR. 49
surrounding iron. The following relation exists between the coefficients and the
deviation:
sin z +C cos z + T> sin 2^+E cos 2z r ,
where d is the deviation, and z the ship s heading by compass, measured from
compass North.
115. MEAN DIRECTIVE FORCE. The effect of the disturbing forces is not confined
to causing deviations ; it is only those components acting at right angles to the needle
which operate to produce deflection; the effect of those acting in the direction of
the needle is exerted either in increasing or diminishing the directive force of the
compass, according as the resolved component is northerly or southerly.
It occurs, with the usual arrangement of iron in a vessel, that the mean effect
of this action throughout a complete swing of the ship upon all headings is to reduce
the directive force that is, while it varies with the heading, the average value upon
all azimuths is minus or southerly. The result of such a condition is unfavorable
from the fact that the compass is thus made more " sluggish," is easily disturbed
and does not return quickly to rest, and a given deflecting force produces a greater
deviation when the directive force is reduced. The usual methods of compensation
largely correct this fault, but do not entirely do so ; it is therefore the case that the
mean combined horizontal force of earth and ship to north is generally less than the
horizontal force of the earth alone; but it is only in extreme cases that this deficiency
is serious.
116. HEELING ERROR. This is an additional cause of deviation that arises
when the vessel heels to one side or the other. Heretofore only those forces have
been considered which act when the vessel is on an even keel; but if there is an incli
nation from the vertical certain new forces arise, and others previously inoperative
become effective. These forces are (a) the vertical component of the subpermanent
magnetism acquired in building; (b) the vertical component of the induced magnetism
in vertical soft iron, and (c) the magnetism induced by the vertical component of
the earth s total force in iron which, on an even keel, was horizontal. The first two
of these disturbing causes are always present, but, when the ship is upright, have no
tendency to produce deviation, simply exerting a downward pull on one of the poles
of the needle; the last is a new force that arises when the vessel heels.
The maximum disturbance due to heel occurs when the ship heads North or
South. When heading East or West there will be no deviation produced, although
the directive force of the needle will be increased or diminished. The error will
increase with the amount of inclination from the vertical.
117. For the same reason as was explained in connection with semicircular
deviations, that part of the heeling error due to subpermanent magnetism will vary,
on change of latitude, as YJ> while that due to vertical induction will vary as tan 0.
In south magnetic latitude the effect of vertical induction will be opposite in direction
to what it is in north latitude.
118. The heeling error is corrected by a permanent magnet placed in a vertical
position directly under the center of the compass. Such a magnet has no effect upon
the compass when the ship is upright ; but since its force acts in an opposite direction
to the force of the ship which causes heeling error, is equal to the latter in amount,
and is exerted under the same conditions, it affords an effective compensation. For
similar reasons to those affecting the compensation of B and C, the correction by
means of a permanent magnet is not general and must be rectified upon change of
latitude.
PRACTICAL COMPENSATION.
119. In the course of explanation of the different classes of deviation occasion
has been taken to state generally the various methods of compensating the errors that
are produced. The practical methods of applying the correctors wiu next be given.
120. ORDER OF CORRECTION. The following is the order of steps to be followed
in each case. It is assumed that the vessel is on an even keel, that the compass is
properly centered in the binnacle, that all surrounding masses of iron or steel are in
their normal positions, all correctors removed, and that the binnacle is one in which
61828 16 - 4
50 THE COMPASS EBROB.
the semicircular deviation is corrected by two sets of permanent magnets at right
angles to each other.
In order to ascertain if the compass is properly centered in the binnacle, the
heeling corrector may be temporarily placed in its tube and drawn from its lowest
to its nighest position; if no deflection is shown by the needle the compass is prop
erly centered; if not it should be adjusted by the screws provided for the purpose.
1 . Place quadrantal correctors by estimate.
2. Correct semicircular deviation.
3. Correct quadrantal deviation. _
4. Swin^ ship for residual deviations.
The heeling corrector may be placed at any time after the semicircular and
quadrantal errors are corrected. A Flinders bar can be put in place only after
observations in two latitudes.
121. The ship is first placed on some magnetic cardinal point. If North or
South, the only force (theoretically speaking) which tends to produce deflection of the
needle will be the athwartship component of the semicircular force, whose effect is
represented by the coefficient C. It East or West, the only deflecting force will be
the fore-and-aft component of the semicircular force, whose effect is represented by
the coefficient B. This will be apparent from a consideration of the direction of the
forces producing deviation, and is also shown by the equation connecting the terms
(where A and E are zero) :
d = B sin z f + C cos z + D sin 2z .
If the ship is headed North or South, z being equal to or 180, the equation
becomes d = C. If on East or West, z being 9(T or 270, we have d = B.
This statement is exact if we regard only the forces that have been considered
in the problem, but experience has demonstrated that the various correctors when
in place create certain additional forces by their mutual action, and in order to correct
the disturbances thus accidentally produced, as well as those due to regular causes,
it is necessary that the magnetic conditions during correction shall approximate as
closely as possible to those that exist when the compensation is completed; therefore
the quadrantal correctors should first be placed on their arms at the positions which
it is estimated that they will occupy later when exactly located. An error in the
estimate will have but slight effect under ordinary conditions. It should be under
stood that the placing of these correctors has no corrective effect while the ship is on
a cardinal point. Its object is to create at once the magnetic field with which we
shall have to deal when compensation is perfected.
This having been done, proceed to correct the semicircular deviation. If the
ship heads North or South, the force producing deflection is, as has been stated, the
athwartship component of the semicircular force, which is to be corrected by perma
nent magnets placed athwartships ; therefore enter in the binnacle one or more such
magnets, and so adjust their height that the heading of the ship by compass shall
agree with the magnetic heading. When this is done all the deviation on that
azimuth will be corrected.
Similarly, if the ship heads East or West, the force producing deviation is the
fore-and-aft component of the semicircular force, and this is to be corrected by
entering fore-and-aft permanent magnets in the binnacle and adjusting the height
so that the deviation on that heading disappears.
With the deviation on two adjacent cardinal points corrected, the semicircular
force has been completely compensated. Next correct the quadrantal deviation.
Head the ship NE., SE., SW., or NW. The coefficients B and C having been reduced
to zero by compensation, and 2z f , on the azimuths named, being equal to 90 or 270,
the equation becomes d = D. The soft-iron correctors are moved in or out from
the positions in which they were placed by estimate until the deviation on the heading
(all of which is due to quadrantal force) disappears. The quadrantal disturbing
force is then compensated.
122. DETERMINATION OF MAGNETIC HEADINGS. To determine when a ship
is heading on any given magnetic course, and thus to know when the deviation has
been corrected and the correctors are in proper position, four methods are available:
THE COMPASS ERROR. 51
(a) Swing the ship and obtain by the best available method the deviations on a
sufficient number of compass courses to construct a curve on the Napier diagram
for one quadrant, and thus find the compass headings corresponding to two adjacent
magnetic cardinal points and the intermediate intercardinal point, as North, NE.,
and East, magnetic. Then put the ship successively on these courses, noting the
corresponding headings by some other compass, and when it is desired to head on
the various magnetic azimuths during the process of correction the ship may be
steadied upon them by the auxiliary compass. Variations of this method will suggest
themselves and circumstances may render their adoption convenient. The compass
courses corresponding to the magnetic directions may be obtained from observations
made with the auxiliary compass itself, or while making observations with another
compass the headings by the auxiliary may be noted and a curve for the latter
constructed, as explained in article 95, and the required headings thus deduced.
(6) By the methods to be explained hereafter (Chap. XIV), ascertain in advance
the true bearing of the sun at frequent intervals during the period which is to be
devoted to the compensation of the compasses; apply to these the variation and
obtain the magnetic bearings ; record the times and bearings in a convenient tabular
form, or, better still, plot a curve of magnetic azimuths of the sun on cross section paper,
the coordinates being local apparent time and magnetic bearings of the sun, as described
in article 89. Set the watch accurately for the local apparent time; then when it
is required to steer any given magnetic course, set that point of the pelorus for the
ship s head and set the sight vanes for the magnetic bearing of the sun corresponding
to the time by watch. Maneuver the ship with the helm until the sun comes on the
sight vanes, when the azimuth of the ship s head will be that which is required. The
sight vanes must be altered at intervals to accord with the curve or table of times
and bearings.
(c) Construct a curve or table showing times and corresponding magnetic
bearings of the sun, and also set the watch, as explained for the previous method.
Then place the sight vanes of the azimuth circle of the compass at the proper angular
distance to the right or left of the required azimuth of the ship s head ; leave them so
set and maneuver the ship with the helm until the image of the sun comes on with
the vanes. The course will then be the required one. As an example, suppose that
the curve or table shows that the magnetic azimuth of the sun at the time given by
the watch is N. 87 E., and let it be required to head magnetic North; when placed
upon this heading, therefore, the sun must bear 87 to the right or east of the
direction of the ship s head; when steady on any course, turn the sight vane to the
required bearing relative to the keel. It on N. 11 W., for example, turn the circle
to N. 76 E.; leave the vane undisturbed and alter course until the sun comes on.
The magnetic heading is then North, and adjustment may be made accordingly.
(d) When ranges are available, they may be utilized for determining magnetic
headings.
123. SUMMARY OF ORDINARY CORRECTIONS. To summarize, the following is
the process of correcting a compass for a single latitude, where magnets at right
angles are employed for compensating the semicircular deviation and where the dis
turbances due to unsymmetrical soft iron are small enough to be neglected.
First. All correctors being clear of the compass, place the quadrantal correctors
in the position which it is estimated that they will occupy when adjustment is com
plete. The navigator s experience will serve in making the estimate, or if there
seems no other means of arriving at the probable position they may be placed at the
middle points of their supports.
Second. Steady the ship on magnetic north, east, south, or west, and hold on
that heading by such method as seems best. By means of permanent magnets alter
the indications of the compass until the heading coincides with the magnetic course.
If heading north, magnets must be entered north ends to starboard to correct easterly
deviation and to port to correct westerly, and the reverse if heading south. If
heading east, enter north ends forward for easterly and aft for westerly deviations,
and the reverse if heading west. (Binnacles differ so widely in the methods of carry
ing magnets that details on this point are omitted. It may be said, however, that
o This is all that is required for the purposes of compensation, but if there is opportunity it is always well to make a complete
swing and obtain a full table of deviations, which may give interesting information of the existing magnetic conditions.
52 THE COMPASS ERROR.
the magnetic intensity of the correctors may be varied by altering either their number
or their distance from the compass; generally speaking, several magnets at a dis
tance are to be preferred to a small number close to the compass.)
Third. Steady the ship on an adjacent magnetic cardinal point and correct the
compass heading by permanent magnets to accord therewith in the same manner as
described for the first heading.
Fourth. Steady the ship on an intercardinal point (magnetic) and move the
quadrantal correctors away from or toward the compass, keeping them at equal
distances therefrom, until the compass and magnetic headings coincide.
Fifth. If time permits, it is very important that the ship should next be steadied
on opposite cardinal and semicardinal points and one-half 01 the remaining deviation
corrected by changing the position or number of the correctors.
The compensation being complete, the navigator should proceed immediately
to swing ship and make a table of the residual deviations. Though the remain
ing errors will be small, it is seldom that they will be reduced to zero, and it must
never be assumed that the compass may be relied upon without taking the devi
ation into account. Observations on eight equidistant points will ordinarily
suffice for this purpose.
124. COMPENSATION OF THE COMPASS WHILE CRUISING. Every effort should
be made to keep at least the standard and steering compasses compensated, as it is
always easier to keep- the compasses compensated than to keep a deviation table
correct, at hand, and in use.
RECTANGULAR METHOD.
By the following method the compasses may be kept practically compensated
and, after the data are once obtained, it requires very little time or trouble.
After the first compensation is completed, or while it is being done, head the
ship north or south and move the athwartship magnets up exactly 1 inch, noting
by the bearing of the sun or of a distant .object, the amount and direction of the
effect on the compass. Then repeat the observation, lowering the magnets 1 inch,
and noting the effect. Then head the ship east or west and take the same obser
vations with the fore-and-aft magnets. Then head on an intercardinal point and
record the effect of moving spheres first in and then out an inch from the correct
position.
The record would then take this form:
Date Latitude Longitude
H e
On North, raising B magnets (6 bundles) 1 inch (from 9.85 to 8.85) causes 12 30 Easterly deviation,
therefore a movement of ^ inch causes 1 15 Ely.
Lowering B magnets (6 bundles) 1 inch (from 9.85 to 10.85) causes 10 15 Westerly deviation,
therefore a movement of -^ inch causes 1 2 / Wly.
On East, raising G magnet (2 bundles) 1 inch (from 10.45 to 9.45) causes 8 15 Westerly deviation,
therefore a movement of ^ inch causes 50 Wly.
Lowering C magnet (2 bundles) 1 inch (from 10.45 to 11.45) causes 6 30 Easterly deviation,
therefore a movement of ^ inch causes 39 Ely.
On Northeast, moving spheres in 1 inch (from 10.6 to 9.6) causes 4 15 Westerly deviation, therefore a
movement of ^ inch causes 25 Wly.
Moving spheres out 1 inch (from 10.6 to 11.6) causes 3 20 7 Easterly deviation, therefore a move
ment of ^j- inch causes 20 Ely.
If now it is^found at any time that there is, say, 1 45 Easterly on East, it is
evident that raising the C magnets -f$ inch will correct it, and careful observations on
two adjacent cardinal points and an inter-cardinal point are enough to recompensate.
This may ordinarily be done at no expense of time and with little trouble. More
confidence may be felt in the result if observations for deviations are afterwards
obtained on the four cardinal points and the mean of the results on opposite courses
taken for the true value; this must be done if the variation is uncertain. A new
set of data observations should be taken after a large change of magnetic latitude,
but it will usually be found that the changes are slight.
Theoretically the quadrantal deviation, once corrected, should remain at zero.
It will usually be found, however, that the position of the spheres must be changed
THE COMPASS ERROR. 53
with change of latitude. A convenient way of dealing with this is to construct a
curve showing the positions of the spheres for varying values of H. A similar curve
showing the position of the heeling magnet is also convenient.
Whenever the position of any corrector is changed, a note showing new position,
date, latitude, longitude, H and 6 should be made on one of the blank leaves of the
compass record. A complete record of this kind will be found of the utmost value
in keeping track of the compasses.
125. CORRECTING THE HEELING ERROR. The heeling error may be corrected
by a method involving computation, together with certain observations on shore.
A more practical method, however, is usually followed, though its results may be less
precise. The heeling corrector is placed in its vertical tube, N. end uppermost in
north latitudes, as this is almost invariably the required direction; the ship being on
a course near North or South and rolling, observe the vibrations of the card, which,
if the error is material, will be in excess of those due to the ship s real motion in
azimuth; slowly raise or lower the corrector until the abnormal vibrations disappear,
when the correction will be made for that latitude; but it must be readjusted upon
any considerable change of geographical position.
In making this observation care must be taken to distinguish the vessel s
yawing" in a seaway from the apparent motion due to heeling error; for this
reason it may be well to have an assistant to watch the ship s head and keep the
adjuster informed of the real change in azimuth, by which means the latter may
better judge the effect of the heeling error.
In the case of a sailing vessel, or one which for any reason maintains a nearly
steady heel for a continuous period, the amount of the heeling error may be exactly
ascertained by observing the azimuth of the sun, and corrected with greater accuracy
than is possible with a vessel which is constantly rolling.
126. FLINDERS BAR. The simplest method that presents itself for the placing
of the Flinders bar is one which is available only for a vessel crossing the magnetic
ec-uator. Magnetic charts of the world show the geographical positions at which the
dip becomes zero that is, where a freely suspended needle is exactly horizontal and
where there exists no vertical component of the earth s total magnetic force. In such
localities it is evident that the factor of the semicircular deviation due to vertical
induction disappears and that the whole of the existing semicircular deviation arises
from subpermanent magnetism. If, then, w^hen on the magnetic equator the compass
be carefully compensated, the effect of the subpermanent magnetism will be exactly
opposed by that of the semicircular correcting magnets. Later, as the ship departs
from the magnetic equator, the semicircular deviation will gradually acquire a
material value, which will be known to be due entirely to vertical induction, and if
the Flinders bar be so placed as to correct it, the compensation of the compass will
be general for all latitudes.
In following this method it may usually be assumed that the soft iron of the
vessel is symmetrical with respect to the fore-and-aft line and that the Flinders bar
may be placed directly forward of the compass or directly abaft it, disregarding the
effect of components to "starboard or port. It is therefore merely necessary to
observe whether a vertical soft iron rod must be placed forward or abaft the compass
to reduce the deviation, and, having ascertained this fact, to find by experiment the
exact distance at which it completely corrects the deviation.
The Flinders bar frequently consists of a bundle of soft iron rods contained in
a case, which is secured in a vertical position near the compass, its upper end level
with the plane of the needles; in this method, the distance remaining fixed, the
intensity of the force that it exerts is varied by increasing or decreasing the number
of rods ; this arrangement is more convenient and satisfactory than the employment
of a single rod at a variable distance.
The United States Navy Flinders bar, Type II, is made of carefully annealed
pure soft iron, 2 inches in diameter, total length 24 inches, consisting of pieces 12
inches, 6 inches, 3 inches, 1 J inches, and inch (2 of these) long. Hardwood blocks
of the same dimensions are used to support the proper length of Flinders bar at the
top of a fixed brass tube, which is secured ordinarily at the forward end of the bin
nacle in the fore-and-aft line.
54 THE COMPASS ERROR.
It should be noted, however, that it is extremely difficult to get soft iron rods
of a satisfactory quality, for, after being placed, they seldom fail to take up more
or less subpermanent magnetism. This magnetism, due to shock of gunfire, vibra
tion while cruising or on speed trials, etc., is subject to greater and more erratic
changes than that of the harder portion of the hull, and its proximity to the compass
intensifies the effect of the variations in its magnetic properties.
127. When it is not possible to correct the compass at the magnetic equator
there is no ready practical method by which the Flinders bar may be placed; the
operation will then depend entirely upon computation, and as a mathematical
analysis of deviations is beyond the scope laid out for this work the details of pro
cedure will not be gone into; the general principles involved are indicated, and
students seeking more must consult the various works that treat the subject fully.
It has been explained that each coefficient of semicircular deviation (B and C)
is made up of a subpermanent factor varying as jj and of a vertical induction factor
varying as tan 0. If we indicate by the subscripts s and v , respectively, the parts due
to each force, we may write the equations of the coefficients:
; and
tr-v tan d.
Now if we distinguish by the subscripts 1 and 2 the values in the first and in the
second position of observation, respectively, of those quantities that vary with the
magnetic latitude, we have :
B. X TT- + B V X tan #!,
**t
and
C 2 = C 8 X TT- + C v X t an 2 .
-ti 2
The values of the coefficients in both latitudes are found from the observations
made for deviations; the values of the horizontal force and of the dip at each place
are known from magnetic charts; hence we may solve the first pair of equations for
B 8 and B v , and the second pair for C 8 and C v ; and having found the values of these
various coefficients, we may correct the effects of B s and C 3 by permanent magnets
in the usual way and correct the remainder that due to B v and C v by the Flinders
bar.
Strictly, the Flinders bar should be so placed that its repelling pole is at an
angular distance from ahead equal to the "starboard angle" of the attracting pole
of the vertical induced force, this angle depending upon the coefficients B v and C v ;
but since, as before stated, horizontal soft iron may usually be regarded as sym
metrical, C v is assumed as zero and the bar placed in the midship line.
128. To CORRECT ADJUSTMENT ON CHANGE OF LATITUDE. The compensation
of quadrantal deviation, once properly made, remains effective in all latitudes, except
ing as noted in article 110; but unless a Flinders bar is used a correction of the
semicircular deviation made in one latitude will not remain accurate when the
vessel has materially changed her position on the earth s surface. With this in
mind the navigator must make frequent observations of the compass error during
a passage and must expect that the table of residual deviations obtained in the
magnetic latitude of compensation will undergo considerable change as that latitude
THE COMPASS EKKOB. 55
is departed from. The new deviations may become so large that it will be found
convenient to readjust the semicircular correcting magnets. This process is very
simple.
)he athwartship magnets or alter their number until the deviation disappears; thon
steady on East or West (magnetic) and similarly adjust the fore-and-aft magnets,
Swing ship for a new table of residual deviations.
129. It must be borne in mind that the compensation of the compass is not
an exact science and that the only safeguard is unceasing watchfulness on the navi
gator s part. As the ship s iron is partly "hard" and partly "soft," the subper-
manent magnetism may change appreciably from day to day, especially in a new
ship as the magnetism absorbed in building "shakes out." After a ship has been in
service for one or two years, the magnetic conditions may be said to be "settled."
They undergo changes, however, to a greater or less extent, on account of the follow
ing influences or conditions:
(a) Continuous steaming on one general course for several days, especially in
rough weather, or lying alongside a dock on one heading for a long period.
(b) Shock of gunfire, even on a ship that has been in commission for more than
a year, has been Known to introduce an 8 error, which disappeared in the course of
a few days.
(c) Extensive alterations or repairs in the vicinity of the compass. The use of
scaling hammers on a military top caused a 3 change in one of the U. S. S. 6V/-
necticut s compasses.
(d) Steaming with boilers (especially under forced draft) whose funnel is near
the compass has been known to cause a change of more than 10, the retained mag
netism being "cooked out."
(e) On the U. S. S. Oregon, a grounded searchlight circuit caused a change of 9.
(/) Ships have reported changes of as much as 7 when struck by lightning or
after passing through very severe thunderstorms.
The binnacle fittings must be carefully inspected from time to time, to see that
the correctors have not changed position. At least once a year the quadrantal
correctors should be examined for polarity. This can be done by moving them,
one at a time, as close to the compass as practicable and then revolving them slowly
about the vertical axis; if the compass is deflected, the magnetism should be removed
by bringing the sphere to a low red heat and then letting it cool slowly.
Tliere is no excuse for large deviations in a standard or steering compass, and they
should not le allowed to exist.
CHAPTER IV.
PILOTING,
130. Piloting, in the sense given the word by modern and popular usage, is the
; rt of conducting a vessel in channels and harbors and along coasts, where landmarks
,;nd aids to navigation are available for fixing the position, and where the depth of
v/ater and dangers to navigation are such as to require a constant watch to be kept
upon the vessel s course and frequent changes to be made therein.
Piloting is the most important part of navigation and the part requiring the most
t xperience and nicest j udgment. An error in position on the high seas may be rec tified
by later observation, but an error in position while piloting usually results in disaster.
Therefore the navigator should make every effort to be proficient in this important
branch, bearing in mind that a modern vessel is usually safe on the high seas and in
danger when approaching the land and making the harbor.
131. Requisites. The navigator should have ready on approaching the land
the charts of the coast and the largest scale detail charts of the locality at which he
xpects to make his landfall, the sailing directions, and the light and buoy list, all
Corrected for the latest information from the Notices to Mariners and other sources.
The usual instruments employed in navigation should be at hand and in good working
rder. The most important instrument the sounding machine should be in place
and in order at least a day before the land is to be made. The importance of the
sounding machine can not be exaggerated. The latest deviation table for the standard
compass must be at hand.
132. LAYING THE COURSE. Mark a point upon the chart at the ship s position;
then mark another point for which it is desired to steer; join the two by a line drawn
v/ith the parallel ruler, and, maintaining the direction of the line, move the ruler
until its edge passes through the center of the compass rose and note the direction.
f the compass rose indicates Redirections, this will be the true course; and must be
orrected for variation and deviation (by applying each in the opposite direction
o its name) to obtain the compass course; ii it is a magnetic rose, the course need
e corrected for deviation only.
Before putting the ship on any course a careful look should be taken along the
line over which it leads to be assured that it clears all dangers.
133. METHODS OF FIXING POSITION. A navigator in sight of objects whose
positions are shown upon the chart may locate his vessel by any one of the following
lethods: ^(a) cross bearings of two known objects; (b) the bearing and distance of a
nown object; (c) the bearing of a known object and the angle between two known
bjects; (d) two bearings of a known object separated by an interval of time, with
h.e^run during that interval; (e) sextant angles between three known objects.
Besides the foregoing there are two methods by which, without obtaining the precise
^osition, the navigator may assure himself that he is clear of any particular danger.
These are: (f) the danger angle ; (#) the danger bearing.
^ The choice of the method will be governed by circumstances, depending upon
which is best adapted to prevailing conditions.
^ 134. CROSS BEARINGS OF Two KNOWN OBJECTS. Choose two objects whose
position on the chart can be unmistakably identified and whose respective bearings
i rom the ship differ, as nearly as possible by 90; observe the bearing of each, either
by compass or pelorus, taking one as quickly as possible after the other; see that
the ship is on an even keel at the time the observation is made, and, if using the
pelorus, be sure also that she heads exactly on the course for which the pelorus is set.
Correct the bearings so that they will be either true or magnetic, according as they are
to be plotted by the true or magnetic compass rose of the chart that is, if observed
by compass, apply deviation and variation to obtain the true bearing, or deviation
56
PILOTING. 57
only to obtain the magnetic; if observed by pelorus, that instrument should be set
for the true or magnetic heading, according as one or the other sort of reading is
required, and no further correction will be necessary. Draw on the chart, by means
of the parallel rulers, lines which shall pass through the respective objects in the
direction that each was observed to bear. As the ship s position on the chart is
known to be at some point of each of these lines, it must be at their intersection, the
only point that fulfills both conditions.
In figure 13, if A and B are the objects and OA and OB the lines passing through
them in the observed directions, the ship s position will be at O, their intersection.
The plotting of a position from two bearings is
greatly facilitated by the use of a plotter devised by
Lieut. K. A. Koch, United States Navy, as reference to
the compass rose on the chart, the use of parallel rulers,
and the drawing of lines on the chart are obviated. A
brief description of this plotter and its uses is as follows:
All materials except bolt and washers are transparent.
A square (7 by 7 inches) ruled with two series of lines
at right angles about one-half inch apart, and a disk
(7J inches in diameter) marked in degrees are placed
on a central hollow bolt of brass and are capable of
being clamped together with any degree of friction re
quired. Three arms are placed so as to revolve around
the same hollow bolt and can be clamped together in
any position. In order to plot a position from compass
bearings of two objects, and lay off a new course, the FIG. 13.
zero mark of the disk should be revolved to the East
or West of the true North and South line of the square by an amount equal to the
compass error in degrees. Two of the arms are then set by the degrees on the
disk to the two observed compass bearings. The plotter is then manipulated on the
chart until the two arms intersect the objects observed and the vertical lines on the
square are parallel to the meridians of the chart. Mark the point of intersection of
the arms by inserting a pencil in the hollow central bolt. An arm may then be swung
to intersect any object 011 the chart and the compass course to that object read from
the disk. This plotter can also be used to obtain the error of the compass from
bearings of three objects by compass.
135. If it be possible to avoid it, objects should not be selected for cross
bearings which subtend an angle at the ship of less than 30 or more than 150, as,
when the lines of bearing approach parallelism, a small error in an observed bearing
gives a large error in the result. For a similar reason objects near the ship should be
taken in preference to those at a distance.
136. When a third object is available a bearing of that may be taken and plotted.
If this line intersects at the same point as the other two (as the bearing OC of the
object C in the figure), the navigator may have a reasonable assurance that his "fix"
is correct; if it does not, it indicates an error somewhere, and it may have arisen from
inaccurate observation, incorrect determination or application of the deviation, or a
fault in the chart.
137. What may be considered as a form of this method can be used when only
one known object is in sight by taking, at the same instant as the bearing, an altitude
of the sun or other heavenly body and noting the
tune; work out the sight and obtain the Sumner
line (as explained in Chapter XV), and the inter
section of this with the direction line from the
object will give the observer s position in the same X)
way as from two terrestrial bearings.
138. BEARING AND DISTANCE OF A KNOWN
OBJECT. When only one object is available, the
ship s position may be found by observing its bear
ing and distance. Follow the preceding method in FlG . 14>
the manner of taking, correcting, and plotting the
bearing; then, on this line, lay off the distance from the object, which will give t
point occupied by the observer. In figure 14, if A represents the object and AO
:ing and distance, the position sought will be at O.
earn
60
PILOTING.
EXAMPLE: A vessel on a course 128 takes the first bearing of an object at
154, and the second at 182, running in the interval 0.8 mile. Required the distance
at which she will pass abeam.
Difference between course and first bearing, 26
Difference between course and second bearing, 54.
Multiplier from second column, Table 5B, 0.76.
0. 8 mile X 0.76 = 0. 6 mile, distance of passing abeam.
145. As has been said, there are certain special cases ot this problem where it is
exceptionally easy of application; these arise when the multiplier is equal to unity
and the distance run is therefore equal to the distance from
the object. When the angular distance on the bow at the
second bearing is twice as great as it was at the first bearing,
the distance of the object from the ship at second bearing is
equal to the run, the multiplier being 1.0. For if, in figure 18,
when the ship is in the first position, O, the object A bears a
on the bow, and at the second position, P, 2a, we have in the
triangle APO, observing that APO = 180 - 2o?, and POA = a :
PAO = 180- (POA+APO),
a.
FIG. 18.
Or, since the angles at O and A are equal to each other, the sides
OP and AP are equal or the distance at second bearing is equal
to the run. This is known as doubling the angle on the low.
146. A case where this holds good is familiar to every
navigator as the ~bow and beam bearing, where the first bearing
is taken when the object is broad on the bow (four points or
45 from ahead) and the second when it is abeam (eight points or 90 from ahead);
in that case the distance at second bearing and the distance abeam are identical
and equal to the run between bearings.
147. When the first bearing is 26J from ahead, and the second 45, the distance
at which the object will be passed abeam will equal the run between bearings. This
is true of any two such bearings whose^ natural cotangents ^ differ by unity, and
the following table is a collection of solutions of this relation in which the pairs of
bearings are such that, when observed in succession from ahead upon the same fixed
object, the distance run between the bearings will be equal to the distance of the fixed
object when it bears abeam, provided that a steady course has been steered, unaffected
by current or drift.
The marked pairs will probably be found the most convenient ones to use, as
they involve whole degrees only.
Bearings from ahead.
First.
Second.
First.
Second.
First.
Second.
20
29|
28
48
37
71f
21
811
*29
51
38
74*
*22
34
30
53f
39
76}
23
36
31
56-1-
*40
79
24
38|
*32
59
41
811
*25
41
33
61|
42
83
26
43|
34
64|
43
85}
26J
45
35
66f
*44
88
*27
46
36
69i
*45
90
When the fixed object bears as per any entry of the first column, take the time
and the reading of the patent log. Repeat this procedure on reaching the bearing of
the adjacent entry in the second column. The difference of the patent-log readings
will be the distance at which the fixed object will be passed abeam.
PILOTING.
61
This general solution includes the 26-45 rule as well as the seven-tenths rule
to be explained later; furthermore, it has the advantage that the approximate
determination of the distance offshore, at which the fixed object will be passed,
need not wait for the 45 bearing. There are two whole-degree pairs bv which such
a determination can be made before the 45 bearing is reached. It is possible to
get five whole-degree bearings or observations by the time the fixed object bears 30
forward of the beam, as follows: 22-34, 25-41, 27-46, 29-51, 32-59. Of
these, the last three should be reasonably accurate; the acuteness of the first angle
in all such observations accounts for the discrepancies noted in practice. The use
of the table given above may be found to be more convenient than the methods of
plotting about to be described, and the use of tables 5A and 5B; but it does not take
the place of those methods. Tables 5A and 5B coyer all combinations of bearings in
which the first bearing is taken when the object is 20 or more on the bow.
The Seven-tenths Rule. If bearings of the fixed object be taken at two (2)
and four (4) points on the bow (22 J and 45), seven-tenths (0.7) of the run between
"bearings will be the distance at which the point will be passed abeam.
From the combination of the seven-tenths rule and the 26^-45 rule, there
follows an interesting corollary, i. e., if bearings of an object at 22^ and 26^ on the
bow be taken, then seven-thirds (J) of the distance run in the interval will be the
distance when abeam.
If a bearing is taken when an object is two points (22 ) forward of the beam
and the run until it bears abeam is measured, then its distance when abeam is seven-
thirds (-J) of the run. This rule, particularly, is only approximate.
In case the 45 bearing on the bow is lost, in order to find the distance abeam
that the object is passed, note the time when the object bears 26^ forward of the
beam, and again when it has the same bearing abaft the beam; the distance run in
this interval is the distance of the object when it was abeam.
To steer an arc course in order to round a light, point, or other object without
fixes and be sure the course itself does not decrease the initial distance: Provided
there is no current, stand on course until the light is at the required distance, deter
mined by one or more of the methods described. Immediately bring the light
abeam, and dp not let it get forward of the beam again, then the course wih 1 not
decrease the initial distance. When the light is onerhalf point abaft the beam
again bring it abeam; hold course until it is again
one-half point abaft the beam, repeating this pro
cedure until the light is rounded. A polygon is thus
circumscribed about the circle, the nearest approach
to the light being the radius of the inscribed circle.
The number of sides of the polygon may be in
creased indefinitely, so that the light may be rounded,
by changing the course just enough to keep the light
abeam, after it is Jirst brought abeam.
148. There is a graphic method of solving this
problem that is considered by some more convenient
than^the use of multipliers. Draw upon the chart
the lines OA and PA (fig. 19), passing through the
object on the two observed bearings; set the dividers
to the distance run, OP; lay down the parallel rulers
in a direction parallel to the course and move them
toward or away from the observed object until some
point is found where the distance between the lines
of bearing is exactly equal to the distance between
the points of the dividers; in the figure this occurs
when the rulers lie along the line OP, and therefore O represents the position of
the ship at the first bearing and P at the second. For any other positions O P ,
O"P", the condition is not fulfilled.
149. Another graphic solution is given by the Mooring and Maneuvering Board
and the various moclificatlons of it that are in use among navigators.
150. The method of obtaining position by two bearings of the same object is
one of great value, by reason of the fact that it is frequently necessary to locate the
ship when there is but one landmark in sight. Careful navigators seldom, if ever,
FIG. 19.
60
PILOTING.
EXAMPLE: A vessel on a course 128 takes the first bearing of an object at
154, and the second at 182, running in the interval 0.8 mile. Required the distance
at which she will pass abeam.
Difference between course and first bearing, 26
Difference between course and second bearing, 54.
Multiplier from second column, Table 5B, 0.76.
0. 8 mile X 0.76 = 0. 6 mile, distance of passing abeam.
145. As has been said, there are certain special cases ot this problem where it is
exceptionally easy of application; these arise when the multiplier is equal to unity
and the distance run is therefore equal to the distance from
the object. When the angular distance on the bow at the
second bearing is twice as great as it was at the first bearing,
the distance of the object from the ship at second bearing is
equal to the run, the multiplier being 1.0. For if, in figure 18,
when the ship is in the first position, O, the object A bears a
on the bow, and at the second position, P, 2a, we have in the
triangle APO, observing that APO = 180 - 2a, and POA
a:
PAO = 180-(POA + APO),
FIG. 18.
Or, since the angles at O and A are equal to each other, the sides
OP and AP are equal or the distance at second bearing is equal
to the run. This is known as doubling the angle on the bow.
146. A case where this holds good is familiar to every
navigator as the "bow and beam bearing, where the first bearing
is taKen when the object is broad on the bow (four points or
45 from ahead) and the second when it is abeam (eight points or 90 from ahead) ;
in that case the distance at second bearing and the distance abeam are identical
and equal to the run between bearings.
147. When the first bearing is 26^ from ahead, and the second 45, the distance
at which the object will be passed abeam will equal the run between bearings. This
is true of any two such bearings whose natural cotangents differ by unity, and
the following table is a collection of solutions of this relation in which the pairs of
bearings are such that, when observed in succession from ahead upon the same fixed
object, the distance run between the bearings will be equal to the distance of the fixed
object when it bears abeam, provided that a steady course has been steered, unaffected
by current or drift.
The marked pairs will probably be found the most convenient ones to use, as
they involve whole degrees only.
Bearings from ahead.
First.
Second.
First.
Second.
First.
Second.
O
20
29f
28
48
37
n f
21
31f
*29
51
38
74}
*22
34
30
53f
39
76|
23
36}
31
56}
*40
79
24
38|
*32
59
41
81}
*25
41
33
61^
42
26
43J
34
64}
43
85}
26i
45
35
66f
*44
88
*27
46
36
69}
*45
90
When the fixed object bears as per any entry of the first column, take the time
and the reading of the patent log. Kepeat this procedure on reaching the bearing of
the adjacent entry in the second column. The difference of the patent-log readings
will be the distance at which the fixed object will be passed abeam.
PILOTING.
61
This general solution includes the 26-45 rule as well as the seven-tenths rule
to be explained later; furthermore, it has the advantage that the approximate
determination of the distance offshore, at which the fixed object will be passed,
need not wait for the 45 bearing. There are two whole-degree pairs by which such
a determination can be made before the 45 bearing is reached. It is possible to
get five whole-degree bearings or observations by the time the fixed object bears 30
forward of the beam, as follows: 22-34, 25-41, 27-46, 29-51, 32-59. Of
these, the last three should be reasonably accurate; the acuteness of the first angle
hi all such observations accounts for the discrepancies noted in practice. The use
of the table given above may be found to be more convenient than the methods of
plotting about to be described, and the use of tables 5A and 5B; but it does not take
the place of those methods. Tables 5A and 5B coyer all combinations of bearings in
which the first bearing is taken when the object is 20 or more on the bow.
The Seven-tenths Rule. If bearings of the fixed object be taken at two (2)
and four (4) points on the bow (22J and 45), seven-tenths (0.7) of the run between
"bearings will be the distance at which the point will be passed abeam.
From the combination of the seven-tenths rule and the 26i-45 rule, there
follows an interesting corollary, i. e., if bearings of an object at 22^ and 26J on the
bow be taken, then seven-thirds (-J) of the distance run in the interval will be the
distance when abeam.
If a bearing is taken when an object is two points (22) forward of the beam
and the run until it bears abeam is measured, then its distance when abeam is seven-
thirds (-J) of the run. This rule, particularly, is only approximate.
In case the 45 bearing on the bow is lost, in order to find the distance abeam
that the object is passed, note the tune when the object bears 26J forward of the
beam, and again when it has the same bearing abaft the beam; the distance run in
this interval is the distance of the object when it was abeam.
To steer an arc course in order to round a light, point, or other object without
fixes and be sure the course itself does not decrease the initial distance: Provided
there is no current, stand on course until the lig;ht is at the required distance, deter
mined by one or more of the methods described. Immediately bring the light
abeam, and dp not let it get forward of the beam again, then the course will not
decrease the initial distance. When the light is onerhalf point abaft the beam
again bring it abeam; hold course until it is again
one-half point abaft the beam, repeating this pro
cedure until the light is rounded. A polygon is thus
circumscribed about the circle, the nearest approach
to the light being the radius of the inscribed circle.
The number of sides of the polygon may be in
creased indefinitely, so that the light may be rounded,
by changing the course just enough to keep the light
abeam, after it is first brought abeam.
148. There is a graphic method of solving this
problem that is considered by some more convenient
than the use of multipliers. Draw upon the chart
the lines OA and PA (fig. 19), passing through the
object on the two observed beanngs; set the dividers
to the distance run, OP; lay down the parallel rulers
in a direction parallel to the course and move them
toward or away from the observed object until some
point is found where the distance between the lines
of bearing is exactly equal to the distance between
the points of the dividers; in the figure this occurs
when the rulers lie along the line OP, and therefore O represents the position of
the ship at the first bearing and P at the second. For any other positions O P ,
O"P", the condition is noMulfilled.
149. Another graphic solution is given by the Mooring and Maneuvering Board
and the various modifications of it that are in use among navigators.
150. The method of obtaining position by two bearings of the same object is
one of great value, by reason of the fact that it is frequently necessary to locate the
ship when there is but one landmark in sight. Careful navigators seldom, if ever,
FIG. 19.
62 PILOTING.
miss the opportunity for a bow and beam bearing in passing a lighthouse or other
well-plotted object; it involves little or no trouble, and always gives a feeling of
addea security, however little the position may be in doubt. If about to pass an
object abreast of which there is a danger a familiar example of which is when a
lighthouse marks a point off which are rocks or shoals a good assurance of clearance
should be obtained before bringing it abeam, either by doubling the angle on the
bow, or, if the object be sighted in time, by using any of the pairs of bearings tabulated
under article 147.
151. It must be remembered that, however convenient, the fix obtained by
two bearings of the same object will be in error unless the course and distance are
correctly estimated, the course "made good" and the distance "over the ground"
being required. Difficulty will occur in estimating the exact course when there is
bad steering, a cross current, or when a ship is making leeway; errors in the allowed
run will arise when she is being set ahead or back by a current or when the logging
is inaccurate. A current directly with the course of the ship, if unallowed for, will
give a determination of position too close to the object observed; and a current*
directly against the course of the ship, if unallowed for, will give a determination of
position too far away from the object observed. The existence of such a current
will not le revealed by taking more than two successive bearings. All such observa
tions will place the ship on the same apparent course, which course will be parallel
to the course made good and to the course steered but in error in its distance from
the observed object by an amount dependent upon the ratio of the speed of ship
over ground to the speed of ship by log. A current oblique to the course of the ship
will give a determination of position which will be erroneous. The existence of
such a current but not its amount will "be revealed by taking more than two observa
tions; in this case, following the usual method of plotting, the determination resulting
from any two successive bearings will fail to agree with the determination from any
other two. If, in such a case, the observed bearings be drawn upon the chart and
the distances run by log between them be laid down on the scale of the chart upon a
piece of paper, a course may be found by trial, upon which course the intervals of
run correspond with the intervals between the lines of bearing. The apparent course
thus determined, which must always be oblique to the course steered, will be parallel
to the course actually being made good, but will be in error in its distance from the
observed object by an amount dependent upon the ratio of the speed of ship over
the ground to the" speed of ship by log. If there is an apparant shortening of the
distance run from earlier to later observations, or a shortening of the time if the
speed is invariable, there is a component of set toward the fixed object. Therefore,
if in a current of any sort, due allowance must be made, and it should be remembered
that more dependence can be placed upon a position fixed by simultaneous bearings
or angles, when two or more objects are available, than by two bearings of a single
object.
152. SEXTANT ANGLES BETWEEN THREE KNOWN OBJECTS. This method,
involving the solution of the three-point problem, will, if the objects be well chosen,
give the most accurate results of any. It is largely employed in surveying, because
of its precision; and it is especially valuable in navigation, because it is not subject
to errors arising from imperfect knowledge of the compass error, improper logging,
or the effects of current, as are the methods previously described.
Three objects represented on the chart are selected and the angles measured
with sextants of known index error between the center one and each of the others.
Preferably there should be two observers and the two angles be taken simultaneously,
but one observer may first take the angle which is changing more slowly, then take
the other, then repeat the first angle, and consider the mean of the first and last
observations as the value of the first angle. The position is usually plotted by
means of the three-armed protractor, or station-pointer (see art. 428, Chap. XVII).
Set the right and left angles on the instrument, and then move it over the chart
until the three beveled edges pass respectively and simultaneously through the
three objects. The center of the instrument will then mark the ship s position, which
may be pricked on the chart or marked with a pencil point through the center hole.
When the three-armed protractor is not at hand, the tracing-paper protractor will
prove an excellent substitute, and may in some cases be preferable to it, as, for
PILOTING. 63
instance, when the objects angled on are so near the observer as to be hidden by
the circle of the instrument. A graduated circle printed upon tracing paper permits
the angles being readily laid off, but a plain piece of tracing paper may be used and
the angles marked by means of a small protractor. The tracing-paper protractor
permits the laying down, for simultaneous trial, of a number of angles, where special
accuracy is sought.
153. The three-point problem, by which results are obtained in this method,
is : To find a point such that three lines drawn from this point to three given points
shall make given angles with each other.
Let A, B, and C, in figure 20, be three fixed objects on shore, and from the
ship, at D, suppose the angles CDB and ADB are found equal, respectively, to 40
and 60
With the complement of CDB, 50, draw the lines BE and CE; the point of
intersection will be the center of a circle, on some point of whose circumference the
ship must be. Then, with the complement of the angle ADB, 30, draw the lines
AF and BF, meeting at F, which point will be the center of another circle, on some
point of whose circumference the ship must be. Then D, the point of intersection
of the circumference of the two circles, will be the position of the ship.
The correctness of this solution mav be seen as follows: Take the first circle,
DEC; in the triangle EBC, the angle" at E^ the center, equals 180-2x50 =
2 (90 50), twice the complement of 50, which is twice the observed angle; now
if the angle at the center subtended by the chord BC equals twice the observed
angle, then the angle at any point on the cir
cumference subtended by that chord, which
equals half the angle, at the center, equals the
observed angle; so the required condition is
fulfilled. Should either 01 the angles exceed
90, the excess of the angle over 90 must be
laid off on the opposite side of the lines joining
the stations.
It may be seen that the intersection of
the circles becomes less sharp as the centers
E and F approach each other; and finally that
the problem becomes indeterminate when the
centers coincide, that is, when the three
observed points and the observer s position all FlG
fall upon the same circle; the two circles are
then identical and there is no intersection; such a case is called a "revolver," because
the protractor will revolve around the whole circle, everywhere passing through the
observed points. The avoidance of the revolver and the*employment of large angles
and short distances form the keys to the selection of favorable objects.
Generally speaking, the observer, in judging which objects are the best to be
taken, can picture in his eye the circle passing through the three points and note
whether it comes near to his own position. If it does, he must reject one or more
of the objects for another or others. It should be remembered that he must avoid
not only the condition where the circle passes exactly through his position (when
the problem is wholly indeterminate), but also all conditions approximating thereto,
for in such cases the circles will intersect at a very acute angle, and the inevitable
small errors of the observation and plotting will produce large errors in the result
ing fix.
Without giving an analysis of reasons, which may be found in various works
that treat the problem in detail, the following may be eniimerated as the general
conditions which result in a good fix:
(a) When the center object of the three lies between the observer and a line
joining the other two, or lies nearer than either of the other two.
(&) When the sum of the right and left angles is equal to or greater than 180.
(c) When two of the objects are in range, or nearly so, and the angle to the third
is not less than 30.
(d) When the three objects are in the same straight line.
64
PILOTING.
FIG. 21.
A condition that limits all of these is that angles should be large at least as
large as 30 excepting in the case where two objects are in range or nearly so, and
then the other angle must be of good size. When possible, near objects should be
used rather than distant ones. The navigator should not fall into the error of
assuming that objects which would give good cuts for a cross bearing are necessarily
favorable for the three-point solution.
In a revolver, the angle formed by lines drawn from the center object to the
other two, added to the sum of the two observed angles, equals 180. A knowledge
of this fact may aid in the choice of objects.
If in doubt as to the accuracy with which the angles will plot, a third angle to
a fourth object may be taken. Another way to make sure of a doubtful fix is to
take one compass bearing, by means of which even
a revolver may be made to give a good position.
154. THE DANGER ANGLE. When sailing along
a coast, to avoid sunken rocks, or shoals, or danger
ous obstructions at or below the surface of the water,
and which are marked on the chart, the navigator
may pass these at any desired distance by using what
is known as a danger angle, of which tnere are two
kinds, namely, the horizontal and vertical danger
angles; the former requires two well-marked objects
indicated on the^chart, lying in the direction of the
coast, and sufficiently distant from each other to
give a fair-sized horizontal angle; the latter requires
a well-charted object of known height.
155. In figure 21, let AMB be a portion of the
coast along which a vessel is sailing on the course
CD; A and B two prominent objects shown on the
chart; S and S are two outlying shoals, reefs, or
dangers. In order to pass outside of the danger S
take the middle point of the danger as a center and the given distance from the
center it is desired to pass as radius, and describe a circle. Pass a circle through
A and B tangent to the seaward side of the first circle. To do this, it is only neces
sary to join A and B and draw a line perpendicular to the middle of AB, and then
ascertain by trial the location of the center of the circle EAB. Measure the angle
AEB, set the sextant to this angle, and remembering that AB subtends the same angle
at all points of the arc AEB, the ship will be outside the arc AEB, and clear the
danger S , as long as AB does not subtend an angle greater than AEB, to which the
sextant is set. At the same time in
order to avoid the danger S, take the
middle point of the danger S and with
the desired distance as a radius de
scribe a circle. Pass a second circle
through A and B tangent to this circle
at G, measure the angle AGB with a
protractor, then, as long as the chord
AB subtends an angle greater than
AGB, the ship will be inside the cir
cle AGB. Therefore, the ship will pass
between the dangers S and S as long
as the angle subtended by AB is less
than AEB and greater than AGB.
156. The vertical danger angle
involves the same general principle, as
can be readily seen without explana
tion by reference to the figure 22 in which AB represents a vertical object of known
height.
157. THE DANGER BEARING. This is a method by which the navigator is warned
by a compass bearing when the course is leading into danger. Suppose a vessel to
be steering a course, as indicated in figure 23, along a coast which must not be
FIG. 22.
PILOTING.
65
approached within a certain distance, the landmark A being a guide. Let the navigator
draw through A the line XA, clear of the danger at all points, and note its direction
by the compass rose; then let frequent bearings be taken as the ship proceeds, and
so long as the bearings, YA, ZA, are to the right of XA he may be assured that he is
on the left or safe side of the line.
If, as in the case given, there is but one object in sight and that nearly ahead, it
would be very difficult to get an exact position, but this method would always show
whether or not the ship was on a good course, and would, in consequence, be of
the greatest value. And even if there were other objects visible by which to get
an accurate fix it would be a more simple matter to note, by an occasional glance
over the sightvane of the pelorus or compass, that the
ship was making good a safe course than to be put to the
necessity of plotting the position each time.
158. It will occasionally occur that two natural objects
will so lie that when in range they mark a danger bearing;
advantage should be taken of all such, as they are easier to
observe than a compass bearing; but if in a locality with
which the navigator nas not had previous acquaintance the
compass bearing of all ranges should be observed and com
pared with that indicated on the chart in order to make^sure
of the identity of the objects. The utility of ranges, either
artificial or natural, as guides in navigation, extends also to
established lines of bearing giving the true or magnetic direc
tion of fixed objects, such as lines of bearing limiting the
sectors of navigational lights.
159. SOUNDINGS. The practice should be followed of
employing one or two leadsmen to take and report soundings
continuously while in shoal water or in the vicinity of dangers.
The soundings must not be regarded as fixing a position, but they afford a check
upon the positions obtained by other methods. An exact agreement with the
soundings on the chart need not be expected, as there may be some little inaccu
racies in reporting the depth on a ship moving with speed through the water, or
the tide may cause a discrepancy, or the chart itself may la ck perfection; but the
soundings should agree in a general way, and a marked departure from the charac
teristic bottom shown on the chart should lead the navigator to verify his position
and proceed with caution; especially is this true if the water is more shoal than
expected.
160. But if the soundings in shallow water when landmarks are in sight
serve merely as an auxiliary guide, those taken (usually with the patent sounding
machine or deep-sea lead) when there exist no other means of locating the position,
fulfill a much more important purpose. In thick weather, when approaching or
running close to the land, and at all tunes when the vessel is in less than 100 fathoms
of water and her position is in doubt, soundings should be taken continuously and
at regular intervals, and, with the character of the bottom, systematically recorded.
By laying the soundings on tracing paper, along a line which represents the track of
the ship according to the scale of the chart, and then moving the paper over the
chart, keeping the various courses parallel to the corresponding directions on the
chart, until the observed soundings agree with those laid down, the ship s position
will in general be quite well determined. While some localities, by the sharpness
of the characteristics of their soundings, lend themselves better than others to
accurate determinations by this method, there are few places where the mariner
can not at least keep out of danger by the indications, even if they tell him no more
than that the tune has come when he must anchor or lie off till conditions are more
favorable.
161. LIGHTS. Before coming within range of a light the navigator should
acquaint himself with its characteristics, so that when sighted it will be recognized.
The charts, sailing directions, and light lists give information as to the color, character,
and range of visibility of the various lights. Care should be taken to note all of
these and compare them when the light is seen. If the light is of the flashing,
61828 If 5
66 PILOTING.
revolving, or intermittent variety the duration of its periods should be noted to
identify it. If a fixed light, a method that may be employed to make sure that it is
not a vessel s light is to descend several feet immediately after sighting it and observe
if it disappears from view; a navigational light will usually do so, excepting in misty
weather, while a vessel s light will not. The reason for this is that navigational lights
are as a rule sufficiently powerful to be seen at the farthest point to which the ray
can reach without being interrupted by the earth s curvature. They are therefore
seen at the first moment that the ray reaches an observer on a ship s deck, and are
cut off if he lowers the eye. A vessel s light, on the other hand, is usually limited
by its intensity and does not carry beyond a distance within which it is visible at
all heights.
Care must be taken to avoid being deceived on first sighting a light, as there are
various errors into which the inexperienced may fall. The glare of a powerful light
is often seen beyond the distance of visibility of its direct rays by the reflection
downward from particles of mist in the air; the same mist may also cause a white
light to have a distinctly reddish tinge, or it may obscure a light except within short
distances. When a light is picked up at the extreme limit at which the height of
the observer will permit, a fixed light may appear flashing, as it is seen when the
ship is on the crest of a wave, and lost when in the hollow.
Many lights are made to show different colors in different sectors within their
range, and by consulting his chart or books, the navigator may be guided by the
color of the sector in which he finds himself; in such lights one color is generally
used on bearings whence the approach is clear, and another covers areas where
dangers are to be encountered.
The visibility of lights is usually stated for an assumed height of the observer s
eye of 15 feet, and must be modified accordingly for any other height. But it should
be remembered that atmospheric and other conditions considerably affect the visibility,
and it must not be positively assumed, on sighting a light, even in perfectly clear
weather, that a vessel s distance is equal to the range of visibility; it may be either
greater or less, as the path of a ray of light near the horizon receives extraordinary
deflection under certain circumstances; the conditions governing this deflection are
discussed in article 296, Chapter X.
162. BUOYS. While buoys are valuable aids, the mariner should always employ
a certain amount of caution in being guided by them. In the nature of things it is
never possible to be certain of finding buoys in correct position, or, indeed, of finding
them at all. Heavy seas, strong currents, ice, or collisions with passing vessels may
drag them from their places or cause them to disappear entirely, and they are especially
uncertain in unfrequented waters, or those of nations that do not keep a good lookout
upon their aids to navigation. When, therefore, a buoy marks a place where a ship
must be navigated with caution, it is well to have a danger angle or bearing as an
additional guide instead of placing too much dependence upon the buoy being in
place.
Different nations adopt different systems of coloring for their buoys; an
important feature of many such systems, including those adopted by the United
States and various other great maritime nations (though not all), consists in placing
red buoys to be left on the starboard hand of a vessel entering a harbor or fairway,
and black buoys on the port hand. In these various systems the color and character
of the buovs are such as to denote the special purpose for which they aro employed.
163. FOGS AND FOG SIGNALS. As with fights, the navigator should, in a fog,
acquaint himself with the characteristics of the various sound signals which he is
likely to pick up, and when one is heard, its periods should be timed and compared
with those givon in the light lists to insure its proper identity.
Experiment has demonstrated that sound is conveyed through the atmosphere
in a very uncertain way; that its intensity is not always increased as its origin is
approached, and that areas within its range at one time, will seem silent at another.
Add to these facts the possibility that, for some cause, the signal may not be working
as it should be, and we have reason for observing the rule to proceed with the utmost
caution when running near the land in a fog.
Although the transmission of sound through water from the submarine bells
that have been installed on many light vessels and at points of danger is much more
PILOTING. 67
certain than the transmission of sound through air and can be received in such a
way by vessels equipped with submerged microphones on each side as to enable the
direction of the submarine bell to be approximately determined, yet the lead continues
to prove an ever-serviceable guide, and should accordingly be in constant use.
The method of plotting soundings described in article 160 will give the most
reliable position that is obtainable. Moreover, the lead will warn the navigator of
the approach to shallow water, when, if his position is at all in doubt, "it is wisest to
to anchor before it becomes too late.
When running slowly in a fog (which caution, as well as the law, requires that
one should do) it must be borne in mind that the relative effect of current is increased;
for instance, the angle of deflection from the course caused by a cross-set is greater at
low than at high speed.
It is worth remembering that when in the vicinity of a bold bluff shore vessels
are sometimes warned of a too close approach by having their own fog signals echoed
back from the cliffs; indeed, from a Knowledge of the velocity of sound (art. 314,
Chap. XI) it is possible to gain some rough idea of the distance in such a case.
When radio-stations, equipped with fog-signaling apparatus, send out simul
taneous radio and sound signals, distances from the sending station can be found
by noting the elapsed interval between the time of arrival of radio signal and sound
signal, and multiplying this interval expressed in seconds by the velocity per second
of sound- in air, or the velocity per second of sound in water, according as the
sound signals are received through air or through water.
By thus determining the distance from a fog-signal station to different positions
between which the course and distance are known, the position of the vessel could
be approximately found in a manner analogous to that wilich would apply in figure 18
if the distances AO and AP were known in addition to the length and direction of OP.
164. TIDES AND CURRENTS. The information relating to the tides given on
the chart and in other publications should be studied, as it is of importance for the
navigator to know not only the height of the tide above the plane of reference of
the chart, but also the direction and force of ttye tidal current.
The plane of reference adopted for soundings varies with different charts;
on a large number it is that of mean low water, and as no plane of reference above that
of mean low water is ever employed the navigator may with safety refer his sound
ings to that level when in doubt.
When traversing waters in which the depth exceeds the vessel s draft by but a
small margin, account must be taken of the fact that strong winds or a high barom
eter may cause the water to fall below even a very low plane of reference. On coasts
where there is much diurnal inequality in the tides, the amount of rise and fall can
not be depended upon, and additional caution is necessary.
A careful distinction should be made between the vertical rise and fall of the
tide, which is marked at the transition periods by a stationary height, or stand, and
the tidal current, which is the horizontal transfer of water as a result of the difference
of level, producing the flood and ebb : and the intermediate condition, or slack. It
seldom occurs that the turn of the tidal stream is exactly coincident with the high
and low water, and in some channels the current may outlast the vertical movement
which produces it by as much as three hours, the effect being that when the water
is at a stand the tidal stream is at its maximum, and when the current is slack the
rise or fall is going on with its greatest rapidity. Care must be taken to avoid con
founding the two.
The effect of the tidal wave in causing currents may be illustrated by two simple
cases:
(1) Where there is a small tidal basin connected with the sea by a large opening.
(2) Where there is a large tidal basin connected with the sea by a small opening.
In the first case the velocity of the current in the opening will have its maximum
value when the height of the tide within is changing most rapidly, i. e., at a time
about midway between high and low water. The water in the basin keeps at approxi
mately the same level as the water outside. The flood stream corresponds with the
rising and the ebb with the falling of the tide.
In the second case the velocity of the current in the opening will have its maxi
mum value when it is high water or low water without, for then there is the greatest
68 PILOTING.
head of water for producing motion. The flood stream begins about three hours
after low water, and the ebb stream about three hours after high water, slack water
thus occurring about midway between the tides.
Along most shores which lack features like bays and tidal rivers, the current
usually turns soon after high water and low water.
The swiftest current in straight portions of tidal rivers is usually in the middle
of the stream, but in curved portions the most rapid current is toward the outer
edge of the curve, and here the water will be deepest. The pilot rule for best water
is to follow the ebb-tide reaches.
Countercurrents and eddies may occur near the the shores of straits, especially in
bights and near points. A knowledge .of them is useful in order that they may be
taken advantage of or avoided.
A swift current often occurs in the narrow passage connecting two large bodies
of water, owing to their considerable difference of level at the same instant. The
several passages between Vineyard Sound and Buzzards Bay are cases in point. In
the Woods Hole Passage the maximum strength of the tidal streams occurs near
high and low water.
Tide rips are made by a rapid current setting over an irregular bottom, as at
the edges of banks where the change of depth is considerable.
Generally speaking, the rise and fall and strength of current are at their mini
mum along straight stretches of coast upon the open ocean, while bays, bights, inlets,
and large rivers operate to augment the tidal effects, and it is in the vicinity of these
that one finds the highest tides and strongest currents. The navigator need there
fore not be surprised in cruising along a coast to notice that his vessel is set more
strongly toward or from the shore in passing an indentation, and that the evidences
of tide will appear more marked as he nears its mouth. Usually more complete data
are furnished in charts and tide tables regarding the rise and fall, and it frequently
occurs that the information regarding the tidal current is comparatively meager; the
mariner must therefore take every means to ascertain for himself the direction and
force of the tidal and other currents 5 either from the set shown between successive
well-located positions of the ship, or by noting the ripple of the water around buoys,
islets, or shoals, the direction in which vessels at anchor are riding, and the various
other visible effects of the current.
Current arrows on the chart must not be regarded as indicating absolutely the
conditions that are to be encountered. They represent the mean of the direction
and force observed, but the observations upon which they are based may not be
complete, or there may be reasons that bring about a departure from the normal
state.
165. CHARTS. The chart should be carefully studied, and among other things
all of its notes should be read, as valuable information may be given in the margin
which it is not practicable to place upon the chart abreast the locality affected.
The mariner will do well to consider the source of his chart and the authority
upon which it is based. He will naturally feel the greatest confidence in a chart
issued by the Government of one of the more important maritime nations which
maintains a well-equipped office for the especial purpose of acquiring and treating
hydrographic information. He should note the character of the survey from which the
chart has been constructed; and, finally, he should be especially careful that the
chart is of recent issue or bears correction of a recent date facts that should always
be clearly shown upon its face.
It is well to proceed with caution when the chart of the locality is based upon
an old survey, or one whose source does not carry with it the presumption of accu
racy. Ev^en if the original survey was a good one, a sandy bottom, in a region
where the currents are strong or the seas heavy, is liable to undergo in time marked
changes; and where the depth is affected by the deposit or removal of silt, as in the
vicinity of the estuaries of large river systems, the behavior is sometimes most capri
cious. Large blank spaces on the chart, where no soundings are shown, may be
taken as an indication that no soundings were made, and are to be regarded with
suspicion, especially if the region abounds in reefs or pinnacle rocks, in which case
only the closest sort of a survey can be considered as revealing all the dangers. All
of these facts must be duly weighed.
PILOTING. 69
When navigating by landmarks the chart of the locality which is on the largest
scale should be used. The hydrography and topography in such charts appear in
greater detail, and a most important consideration bearings and angles may be
plotted with increased accuracy.
To sum up, the navigator must know the exact draft of the ship when
approaching the land. He must make himself familiar with every detail of the
charts he will be required to use and must read the charts in such a way as to be
able to form a mental picture of how the land and the various aids to navigation
will look when sighted, remembering that the position of the sun at different times
of day, or the position of the moon at night, affects the appearance of the land as
presented to tne navigator approaching from seaward. He must be thoroughly
familiar with the day, night, and fog characteristics of all aids to navigation in the
locality. He must know the state of the tide and the force and direction of the
current at all times when in pilot waters. The navigator, in making his plan for
entering a strange port, should give very careful previous study to the chart, and
should carefully select what appear to be the most suitable marks for use, also pro
viding himself with substitutes for use in case those selected as most suitable should
prove unreliable by not being recognized with absolute certainty. It must be
remembered that buoys seen at a distance, in approaching a channel, are often
difficult to place or identify, because all may appear equally distant, though hi
reality far apart. Ranges should be noted, if possible, and tne lines olrawn, both
for leading through the best water in channels and also for guarding against par
ticular dangers. For the latter purpose, safety bearings should in all cases be laid
down where no suitable ranges offer. The courses to be steered in entering should
also be laid down and distances marked thereon. If intending to use the sextant
and danger angle in passing dangers, and especially in passing between dangers,
the danger circles should be plotted and regular courses planned, rather than to run
haphazard by the indications of the angle alone, with the possible trouble to be
apprehended from wild steering at critical points.
The ship s position should not be allowed to be in doubt at any time, even in
entering ports considered safe and easy of access, and should be constantly checked
by continuing to use for this purpose those marks concerning which there can be
no doubt until others are unmistakably recognized.
The ship should ordinarily steer exact courses and follow exact lines as planned
from the chart, changing course at exact points, and, where the distances are con
siderable, her position on the line should be checked at frequent intervals, recording
the time and the reading of the patent log. This is desirable, even where it may
seem unnecessary for safety; because, if running by the eye alone and the ship s
exact position be suddenly required, as in a sudden squall, fixing at that particular
moment might be impossible.
The habit of running exact courses with precise changes of courses will be found
most useful when it is desired to enter port or pass through inclosed waters during
fog by means of the buoys; here safety demands that the buoys be made successively,
to do which requires, if the fog be dense, very accurate courses and careful attention
to the times, rate of speed, and the set of tne current. Failure to make a buoy as
expected leaves no safe alternative but to anchor at once.
It is a useful point to remember that in passing between dangers where there
are no suitable leading marks, as, for instance, between two islands or an island and
the main shore, with dangers extending from both, a mid-channel course may be
steered by the eye alone with great accuracy, as the eye is able to estimate very closely
the position midway between visible objects.
In piloting among coral reefs or banks, a time should be chosen when the sun
will be astern, conning the vessel from aloft or from an elevated position forward.
The line of demarcation between the deep water and the edges of the shoals, which
generally show as green patches, is indicated with surprising clearness. This method
is of frequent application in the numerous passages of the Florida keys.
Changes of course should in general be made by exact amounts, naming the new
course or the amount of the change desired, rather than by ordering the helm to be
put over and then steadying when on the desired heading, with the possibility of the
attention being diverted and so forgetting in the meantime that the ship is still
70 PILOTING.
swinging. The helmsman, knowing just what is desired and the amount of change
to be made, is thus enabled to act more intelligently and to avoid wild steering,
which in narrow channels is a very positive source of danger.
Coast piloting involves the same principles and requires that the ship s positions
be continuously determined or checked as the landmarks are passed. On well-
surveyed coasts there is a great advantage in keeping near the land, thus holding
on to the marks and the soundings, and thereby knowing at all times the position,
rather than keeping offshore and losing the marks, with the necessity of again making
the land from vague positions, and perhaps the added inconvenience of fog or bad
weather, involving a serious loss of time and fuel.
The route should be planned for normal conditions of weather with suitable
variations where necessary in case of fog or bad weather or making points at night,
the courses and distances, in case of regular runs over the same route, being entered
in a notebook for ready reference, as well as laid down on the chart. The danger
circles for either the horizontal or the vertical danger angles should be plotted,
wherever the method can be usefully employed, and the angles marked thereon;
many a mile may thus be saved in rounding dangerous points, with no sacrifice in
safety. Ranges should also be marked in, where useful for positions or for safety,
and also to use in checking the deviation of the compass by comparing, in crossing,
the compass bearing of the range with its magnetic bearing, as given by the chart.
Changes of course will in general be made with mark or object abeam, the posi
tion (a new "departure") being then, as a rule, best and most easily obtained.
In making the land in a fog the sounding machine must be kept going at intervals
of half an hour some hours before it is expected that soundings can be obtained.
Several soundings taken at random will not locate a ship, but on the contrary may
lead to disaster. In using the sounding machine be careful that the man handling
the tube does not invert the tube when taking it from the tube case, as this would
allow water to run toward the closed end of the tube, causing a discoloration of the
coating and thus bring about an incorrect sounding. It is also essential that the
lead be cleanly and freshly armed for each cast. The bottom having been picked up,
a graphic record of the soundings may be laid down in the manner previously described
in paragraph 160 and an approximation made of the position of the ship. Keep a
sharp lookout for any landmarks that might show up during a momentary lifting
of the fog and have keen ears listening for an aerial or submarine fog signal. Having
picked up any such signal, make sure to ascertain exactly what landmark it is.
From now on proceed with caution and determine whether it is better to anchor or
to proceed through the harbor channel in the fog. If, having approached the land
and failed to hear fog signals at the time they were expected to be heard and the
soundings indicate a dangerous proximity to shore, the only safe course is either to
anchor or to stand off. When running slowly in a fog (which caution, as well as
the law, requires that one should do) it must be borne in mind that the relative effect
of current is increased; for instance, the angle of deflection from the course caused
by a cross set is greater at low than at high speed. It is worth remembering that
when in the vicinity of a bold bluff shore vessels are sometimes warned of a too-close
approach by having their own fog signals echoed back from the cliffs ; indeed, from
a knowledge of the velocity of sound it is possible to gain some rough idea of the
distance in such a case. Great caution must be used in approaching a bold coast
in a fog and, unless soundings can be got that will reasonably assure the navigator
of his distance from the coast, the only safe course is to stand off, if the depth of
the water does not permit of anchoring.
The best aids at the disposal of the navigator when running in a fog are the
sounding machine and the hand lead, and the navigator will do well to make great
use of them. Even in clear weather the sounding machine may be a great aid to the
navigator in verifying his position.
In approaching the land and entering harbors, the navigator must bear in mind
that rules of the road in inland waters sometimes differ from those used on the high
sea, and should inform himself of the boundaries of the waters where different rules
of the road obtain.
166. RECORDS. It will be found a profitable practice to pay careful attention
to the recording of the various matter relating to the piloting of the ship. A notebook
PILOTING.
71
should be kept at hand on deck or on the bridge, in which are to be entered all bearings
or angles taken to fix the position, all changes of course, important soundings, and
any other facts bearing upon the navigation. (This book should be different from
the one in which astronomical sights and offshore navigation are worked.) The
entries, though in memorandum form, should be complete; it should be clear whether
bearings and courses are true, magnetic, or by compass; and it is especially important
that the time and patent log reading should be given for each item recorded. The
value of this book will make itself apparent in various directions; it will afford
accurate data for the writing of the ship s log; it will furnish interesting information
for the next run over the same ground ; it will provide a means by which, if the ship
be shut in by fog, rain, or darkness, or if there be difficulty in recognizing landmarks
ahead, the last accurate fix can be plotted and brought forward; and, finally, if
there should be a mishap, the notebook would furnish evidence as to where the
trouble has been.
The chart on which the work is done should also be made an intelligible record,
and to this end the pencil marks and lines should not be needlessly numerous, heavy,
or, long. In plotting bearings, draw lines only long enough to cover the probable
position. Mark intersections or positions by drawing a small circle around them,
and writing neatly abreast them the time and patent log reading. Indicate the
courses and danger bearings by full lines and mark them appropriately, preferably
giving both magnetic (or true) and compass directions. A great number of lines
extending in every direction may lead to confusion; however remote the chance
may seem, the responsibilities of piloting are too serious to run even a small risk.
Finally, on anchoring, record and plot the position by bearings or angles taken
after coming to; observe that the berth is a safe one, or, if in doubt, send a boat to
sound in the vicinity of the ship to make sure.
CHAPTER V.
THE SAILINGS.
167. In considering a ship s position at sea with reference to any other place,
either one that has been left or one toward which the vessel is bound, five terms are
involved the Course, the Distance, the Difference of Latitude, the Difference of
Longitude, and the Departure.* The solutions of the various problems that arise
from the mutual relation of these quantities are called Sailings.
168. KINDS OP SAILINGS. When the only quantities involved are the course,
distance, difference of latitude, and departure, the process is denominated Plane
Sailing. In this method the earth is regarded as a plane, and the operation proceeds
as if the vessel sailed always on a perfectly level surface. When two or more courses
are thus considered, they are combined by the method of Traverse Sailing. It is
evident that the number of miles of latitude and departure can thus be readily
deduced; but, while one mile always equals one minute in difference of latitude, one
mile of departure corresponds to a difference of longitude that will vary with the
latitude in which the vessel is sailing. Plane sailing therefore furnishes no solution
where difference of longitude is considered, and for such solution resort must be had
to one of several methods, which, by reason of their taking account of the spherical
figure of the earth, are called Spherical Sailings.
When a vessel sails on an east or west course along a parallel of latitude, the
method of converting departure into difference of longitude is called Parallel Sailing.
When the course is not east or west, and thus carries the vessel through various
latitudes, the conversion may be made either by Middle Latitude Sailing, in which
it is assumed that the whole run has been made in the mean latitude, or by Mercator
Sailing, in which the principle involved in the construction
T 1 of the Mercator chart (art. 39, Chap. II) is utilized.
Great Circle Sailing deals with the courses and distances
between any two points when the track followed is a great
circle of the terrestrial sphere. A modification of this method
which is adopted under certain circumstances is called Com-
Dist. posite Sailing.
PLANE SAILING.
169. In Plane Sailing, the curvature of the earth being
neglected, the relation between the elements of the rhumb
track joining any two points may be considered from the
plane right triangle formed by the meridian of the place left,
FlG - s 4 - the parallel of the place arrived at, and the rhumb line. In
figure 24, Tis the point of departure; T , the point of destination; Tn, the meridian
of departure; T n, the parallel of destination; and TT , the rhumb line between the
points. Let C represent the course, T f Tn; Dist., the distance, TT ; DL, the dif
ference of latitude, Tn; and Dep., the departure, T n. Then from the triangle
TT n, we have the following :
n De i
sin C =
cos C =
tan C =
For the definition of these terms, see article 6, Chapter I.
72
Dist.
Dep.
THE SAILINGS.
73
From these equations are derived the following formulae for working the various
problems that may arise in Plane Sailing:
Given.
Required.
Formulae.
Course and distance.
f Difference of latitude.
D L =Dist. cos C.
Dep. =Dist. sin C.
-*nC-j&.
& -%
-.-b-
Dep. =D L tan C.
* -&
DL -53%.
i-o-jfr
Dep. =Dist. sin.C.
SinC =?:
D I, =Dist. cos C.
Log D L =log Dist. -flog cos C.
Log Dep. =log Dist. -flog sin C.
Log tan C=log Dep. log D L.
Log Dist. =log Dep. log sin C.
Log Dist. =log D L -log cos C.
Log Dep. =log D L +log tan C.
Log Dist. =log Dep. -log sin C.
Log D L =log Dep. -log tan C.
Log cos C=log D L log Dist.
Log Dep. =log Dist. -flog sin C.
Log sin C =log Dep. log Dist.
Log D L =log Dist.+log cos C.
Difference of latitude
and departure.
Course and difference of
latitude.
Course and departure. . .
Distance and difference
of latitude.
Distance and departure .
f Course
I Distance
fDistance
Departure
fDistance
(Difference of latitude,
f Course...
i
1 Departure
f Course
J
I Difference of latitude.
170. The solution of the plane right triangle may be accomplished either by
Plane Trigonometry, by Traverse Tables, or by construction. If the former method
is adopted, the logarithms of numbers may be found in Table 42, and of the functions
of angles in Table 44. A more expeditious method is available, however, in the
Traverse Tables, which give by inspection the various solutions. Table 1 contains
values of the various parts for each unit of Dist. from 1 to 300, and for each quar
ter-point (2 49 ), of C; Table 2 contains values for each unit of Dist. from 1 to
600, and for each degree of C. The method of solving by construction consists in
laying down the various given terms by scale upon a chart or plain paper, and
measuring thereon the terms required.
171. Of the various problems that may arise, the first two given in the foregoing
table are of much the most frequent occurrence. In the first, the given quantities
are course and distance, and those to be found are difference of latitude and departure;
this is the case where a navigator, knowing the distance run on a given course, desires
to ascertain the amount made good to north or south and to east or west. In the
second case the conditions are reversed; this arises where the course and distance
between two points are to be obtained from their known difference of latitude and
departure.
EXAMPLE: A ship sails SW. by W., 244 miles. Required the difference of latitude and the departure
made good.
By Computation.
Dist. 244 log 2.33739
C 56 15 log cos 9. 74474
DL 135.6 log 2.13213
Dist. 244 log 2.*38739
C 56 15 log sin 9. 91985
Dep. 202.9 log 2.30724
By Inspection.
In Table 1, find the course SW. by W. (5 points); it
occurs at the bottom of the page, therefore take the names
of the columns from the bottom as well; opposite 244 in
the Dist. column will be seen Lat. 135.6 and Dep. 202.9.
74
THE SAILINGS.
EXAMPLE: A ship sails N. 5 E., 188 miles. Required the difference of latitude and the departure.
By Inspection.
Dist. 188 log 2.27416 In Table 2, find the course 5; it occurs at the top of the
C 5 loer cos 9. 99834 page, therefore take the names of the columns from the
top; opposite 188 in the Dist. column will be seen Lat.
DL 187. 3 log 2. 27250 187.3 and Dep. 16.4.
Dist.
C
Dep.
EXAMPLE : A vessel is bound to a port which is 136 miles to the north and 203 miles to the west of
her position. Required the course and distance.
By Computation.
188 log 2. 27416
5 log cos 9. 99834
187. 3 log
188 log
5 log
16. 4 log
2. 27250
2. 27416
sin 8. 94030
1. 21446
Dep.
DL
By Computation.
log
log
203
136
G (N.) 56 11 (W.)
203
Dep.
C
Dist.
56 IV
244.3
By Inspection.
2. 30750 Enter Table 1 and turn the pages until a course
2. 13354 is found whereon the numbers 136 and 203 are
found abreast- each other in the columns marked
log tan 0. 17396 respectively Lat. and Dep. This occurs most nearly
at the course for 5 points, the angle being taken
log 2. 30750 from the bottom, because the appropriate names
log sin 9. 91951 of the columns are found there. The course is
therefore NW. by W. Interpolating for interme-
2. 38799 diate values, ^ the corresponding number in the
Dist. column is about 244.3.
log
EXAMPLE : As a result of a day s run a vessel changes latitude 244 miles to the south and makes a
departure of 171 miles to the east. What is the course and distance made good?
Dep.
C
Dist.
By Computation.
171 log 2. 23300
244 log 2.38739
(S.) 35 02 (E.) log tan 9. 84561
171 log 2.23300
35 02 log sin 9. 75895
By Inspection.
Enter Table 2 and the nearest agreement will be
found on course (S.) 35 (E.), the appropriate names
being found at the top of the page. The nearest
corresponding Dist. is 298 miles.
297.9 log
2. 47405
TRAVERSE SAILING.
172. A Traverse is an irregular track made by a ship in sailing on several different
courses, and the method of Traverse Sailing consists in finding the difference of
latitude and departure corresponding to several courses and distances and reducing
all to a single equivalent course and distance. This is done by determining the
distance to north or south and to east or west made good on each course, taking the
algebraic sum of these various differences of latitude and departure and finding the
course and distance corresponding thereto. The work can be most expeditiously
performed by adopting a tabular form for the computation and using the traverse
tables.
EXAMPLE: A ship sails SSE., 15 miles; SE., 34 miles; W. by S., 16 miles; WNW., 39 miles;
S. by E., 40 miles. Required the course and distance made good.
Courses.
Dist.
N.
S.
E.
W.
SSE.
15
13.9
5.7
SE.
34
24.0
24.0
W. by S.
16
3.1
15.7
WNW.
39
14.9
36.0
S. by E.
40
39.2
7.8
14.9
80.2
37.5
*51.7
14.9
37.5
S. by W.
66.8
65.3
14.2
The result of the various courses is, therefore, to carry the vessel S. by W., 66.8
miles from her original position.
THE SAILINGS.
75
PARALLEL SAILING.
173. Thus far the earth has been regarded as an extended plane, and its spherical
figure has not been taken into account; it has thus been impossible to consider one
of the important terms involved namely, difference of longitude. Parallel Sailing
is the simplest of the various forms of Spherical Sailing, being
the method of interconverting departure and difference of
longitude when the ship sails upon an east or west course,
and therefore remains always on the same parallel of latitude.
In figure 25, T and T are two places in the same latitude;
P, the adjacent pole; TT , the arc of the parallel of latitude
through the two places; MM , the corresponding arc of the
equator intercepted between their meridians PM and PM :
and TT , the departure on the parallel whose latitude is
TCM=OTC, and whose radius is OT.
Let D.Lo represent the arc of the equator MM , which is
the measure of MPM , the difference of longitude of the me
ridians PM and PM ; R, the equatorial radius of the earth,
CM = CT; r, the radius OT of the parallel TT ; and L, the latitude of that parallel.
Then, since TT and MM are similar arcs of two circles, and are therefore
proportional to the radii of the circles, we have:
TT^ = OT. Dep. r
MM CM ; or D.Lo R.
From the triangle COT, r =
Dep. _R cos L
~T
cos L; hence
; or, D.Lo = Dep. sec. L; or/Dep.=D.Lo cos L.
Thus the relations are expressed between minutes of longitude and miles of
departure.
174. Two cases arise under Parallel Sailing: First, where the difference of
longitude between two places on the same parallel is given, to find the departure;
and, second, where the departure is given, to find the difference of longitude.
In working these problems, the computation can be made by logarithms; but
the traverse tables may more conveniently be employed. Remembering that those
tables are based upon the formulae,
DL = Dist. cos C, and Dist. = DL sec C,
we may substitute for the column marked Lat. the departure, for that marked Dist.
the difference of longitude, and for the courses at top and bottom of the page the
latitude. The tables then become available for making the required conversions.
EXAMPLE: A ship in the latitude of 49 W sails directly east until making good a difference of
longitude of 3 30 7 . Required the departure.
By Inspection.
Enter Table 2 with the latitude as C and the difference
of longitude as Dist. As the table is calculated only to
single degrees, we must find the numbers in the pages of
49 and 50 and take the mean. Corresponding to Dist.
210 in the former is Lat. 137.8, and in the latter Lat. 135.0.
The mean, which is the required departure, is 136.4.
EXAMPLES A ship in the latitude of 38 sails due west a distance of 215.5 miles. Required the
difference of longitude.
By Inspection.
L
D.Lo.
By Computation.
49 30 log cos 9. 81254
log
210
2. 32222
Dep. 136.4 log 2.13476
L
Dep.
D.Ix>{ 4
By Computation.
38 log sec 0. 10347
log 2.33345
215.5
273 . 5
33 / .5
log 2.43692
Entering Table 2 with the latitude, 38, as a course,
corresponding with the number 215.5 in column of Lat.,
is 273.5 in the column of Dist. This is therefore the
required difference of longitude, being equal to 4 33 X .5.
MIDDLE LATITUDE SAILING.
175, When a ship follows a course obliquely across the meridian the latitude is
constantly changing, and the method of converting departure and difference of
longitude by Parallel Sailing, just described, ceases to be applicable.
76
THE SAILINGS.
In figure 26, T is the point of departure; T , the point of destination; P, the
by the arc of the equator, MM , intercepted between their meridians. This corre
sponds to a departure Tn in the latitude of T, and to the smaller departure TX in the
higher latitude of T ; but since the vessel neither makes all of the departure in the
latitude T, nor all of it in the latitude T , the departure actually made in the passage
must have some intermediate value between these extremes. Dividing the total
difference of longitude into a number of equal parts MPm lf m 1 Pm 2 , etc., of such small
extent that, for the purposes of conversion, the change of latitude corresponding to
each may be neglected, we nave the total departure made
p up of the sum of a number of small departures, each equal
to the same difference of longitude, but each different from
the other. These will be d^ in the latitude T, d 2 r 2 in
the latitude r lt etc. Hence we have:
1 sec MT+cZ 2 r 2 , sec
s , sec m 2 r 2 , -fete.
m t m f
FIG. 26.
Now, if LL be a parallel of latitude lying midway
between Tn and T %, since there will be as many of the
small parts lying above as below it, and since for moderate
distances the ratio to be employed in the conversion of
departure and difference of longitude may be regarded as
varying directly with the latitude, it may be assumed for
such distances that the sum of all of the different small
departures equals the single departure between the merid
ians measured in the latitude LI/, and therefore that the
departure obtained by the method of plane sailing on any course may be converted
into difference of longitude by multiplying by the secant of the Middle Latitude.
The method of conversion based upon this assumption is denominated Middle
Latitude Sailing, and by reason of its convenience and simplicity is. usually employed
for short distances, such as those covered by a vessel in a day s run.
176. In Middle Latitude Sailing, having found the mean of the latitudes, the
solution is identical with that of Parallel Sailing (art. 173), substituting the Middle
Latitude for the single latitude therein employed.
EXAMPLE: A ship in Lat. 42 30 N., Long. 58 51 W., sails SE. by S., 300 miles. Required the
latitude and longitude arrived at.
From Table 1: Course SE. by S., Dist., 300, we find Lat., 249.4 S. (4 09 .4), Dep., 166.7 E.
Latitude left,
DL,
42 3(X. N. Latitude left, 42 30 N.
4 09 . 4 S. Latitude arrived at, 38 21 N.
Latitude arrived at, 38 20 . 6 N.
Mid. latitude,
2)80 51
40 25 N.
Enter Table 2 with the middle latitude, 40, as a course; the difference of longitude (Dist.) cor
responding to the departure (Lat.) 166.7 is 217.6; entering with 41, it is 220.9; the mean is 219.2 (3
Longitude left,
D.Lo.
58 51/.0 W.
3 39.2E.
Longitude arrived at, 55 11 .8 W.
EXAMPLE: A ship in Lat. 39 42 S., Long. 3 31 E., sails S. 42 W., 236 miles. Required the lati
tude and longitude arrived at.
From Table 2: Course, S. 42 W., Dist., 236 miles; we find Lat., 175.4 S. (2 55 .4), Dep., 157.9 W.
Latitude left, 39 42 . S. Latitude left, 39 42 S
DL, 2- 55 .4 S. Latitude arrived at, 42 37 S.
Latitude arrived at, 42 37 .4 S.
2)82 19
Mid. latitude,
41 09 S.
THE SAILINGS.
77
From Table 2: Mid. Lat. (course), 41, Dep. (Lat.), 157.9; we find D.Lo (Dist.), 209.3 (3 C
Longitude left, 3 31 .0 E.
D.Lo, 3 29.3W.
29 / .3).
Longitude arrived at, 01 .7 E.
EXAMPLE: A vessel leaves Lat. 49 57 N., Long. 15 16 W., and arrives at Lat. 47 18 N., Long.
20 10 7 W. Required the course and distance made good.
Latitude left 49 57 N. Longitude left, 15 16 W.
Latitude arrived at, 47 18 N. Longitude arrived at, 20 10 W.
DT / 2 39 \o "^T / 4 54 \ w
\ 159 j u.ix), | 294 J
2)97 15 X X.
Mid. latitude, 48 38 N.
From Table 2: Mid. Lat. (course), 49, D.Lo (Dist.), 294; we find Dep. (Lat.), 192.9.
From Table 2: DL 159 S., Dep. 192.9 W., we find course S. 51 W., Dist., 251 miles.
177, It may be remarked that the Middle Latitude should not be used when
the latitudes are of opposite name; if of different names and the distance is small,
the departure may be assumed equal to the difference of longitude, since the meridians
are sensibly parallel near the equator; but if the distance is great the two portions
of the track on opposites of the equator must be treated separately.
178. The assumption upon which Middle Latitude sailing is based that the
conversion may be made as if the whole distance were sailed upon a parallel midway
between the latitudes of departure and destination while sufficiently accurate for
moderate distances, may be materially in error where the distances are large. In
such case, either the method of Mercator Sailing (art. 179) must be employed, or else
the correction given in the following table should be applied to the mean latitude to
obtain what may be termed the latitude of conversion, being that latitude in which
the required conditions are accurately fulfilled. The table is computed from the
formula:
cos L r = .
ra
where L c represents the latitude of conversion, and Z and m are respectively the differ
ences of latitude and of meridional parts (art. 40, Chap. II) between the latitudes of
departure and destination.
Mid.
Lat.
Difference of latitude.
Mid.
Lat.
1
2
3
4
5
6
7
8
9
10
12 | 14
16*
18
20
15
18
21
-86
-67
-54
-85
-67
-54
-84
-66
-53
-83
-65
-52
-81
-63
-51
-79
-61
-49
/
-76
-59
-47
/
-73
-56
-44
/
-69
-53
40
/
-65
-50
-39
-56
-43
-32
-i
ifj
/
-34
-23
-15
t
-21
-12
- 5
- 6
1
7
15
18
21
24
30
35
-44
-31
-23
-44
-30
-22
-44
-29
-21
-42
-29
-21
-41
-28
-19
-40
-26
-18
38
--24
-17
-36
-23
-15
-33
-20
-12
-31
-18
-10
-24
-12
- 5
-17
- 6
2
- 8
1
10
1
11
18
12
21
28
24
30
35
40
45
50
-17
-12
- 8
-16
-11
- 8
-15
-11
- 7
-14
-10
- 6
-13
- 8
- 5
-12
- 7
- 3
-10
- 5
- 1
Q
- 3
1
- 6
- 1
3
- 4
I
6
2
7
12
8
14
20
16
22
28
25
31
38
34
41
49
40
45
50
55
58
60
- 5
- 4
- 3
- 5
2
- 3
- 4
- 3
- 2
3
- 1
_ 2
1
2
3
2
4
5
5
7
8
7
10
11
10
13
14
17
20
22
25
29
32
35
39
43
46
51
55
58
64
69
55
58
60
62
64
66
- 3
2
- 2
- 2
- 1
- 1
- 1
1
2
2
3
4
4
5
6
7
8
9
9
11
12
13
14
16
17
18
20
25
27
30
35
38
42
46
50
55
60
65
71
75
81
89
62
64
66
68
70
72
- 1
- 1
1
1
2
2
3
4
5
5
6
7
8
10
10
12
13
g
18
18
20
23
22
25
28
33
37
41
46
51
57
61
67
76
78
87
97
98
109
123
68
70
72
a The statement often made that the latitude of conversion is always greater than the middle latitude is not correct when the
compression of the earth is taken hi to account, as an inspection of the table will show; that statement is based upon an assumption
that the earth is a perfect sphere, and it was upon that assumption that a table which appeared in early editions of this work was
computed. The value of the compression adopted for this table is
78
THE SAILINGS.
EXAMPLE: A vessel sails from Lat. 10 13 S. to Lat. 20 21/ S., making a departure of 432 milee.
Required the difference of longitude.
Latitude left, 10 13 S.
Latitude arrived at, 20 21 S.
Mid. latitude,
Correction,
2)30 34
15 17 S.
- 1 05
For Mid. Lat. 15 and Diff. of Lat. 10. Correction, -65 .
L c , 14 12 S.
L 14 12 log sec .01348
Dep. 432 log 2.63548
D.Lo 445 .6 log 2.64896
MERCATOR SAILING.
179. Mercator Sailing is the method by which values of the various elements
are determined from considering them in the relation in which they are plotted upon
a chart constructed according to the Mercator projection.
180. Upon the Mercator chart (art. 39, Chap. II), the meridians being parallel,
the arc of a parallel of latitude is shown as equal to the corresponding arc of the
equator; the length of every such arc is, therefore, expanded; and, in order that
the rhumb line may appear as a straight line, the meridians are also expanded by
such amount as is necessary to preserve, in any latitude, the proper proportion
existing between a unit of latitude and a unit of longitude. The length of small
portions of the meridian thus increased are called meridional parts (art. 40, Chap. II),
and these, computed for every minute of latitude from to 80, form the Table of
Meridional Parts (Table 3), by means of which a Mercator chart may be constructed
and all problems of Mercator Sailing may be solved.
In the triangle ABC (fig. 27), the angle ACB is the course, C; the side AC, the
distance, Dist.; the side BC, the difference of latitude, DL; and the side AB, the
departure, Dep. Then corresponding to the^ difference of lati
tude BC in the latitude under consideration, if CE be laid off to
represent the meridional difference of latitude, m, completing the
right triangle CEF, EF will represent the difference of longitude,
D.Lo. The triangle ABC gives the relations involved in Plane
Sailing as previously described; th# triangle CEF affords the
means for the conversion of departure and difference of longi
tude by Mercator Sailing.
181. To find the arc of the expanded meridian intercepted
between any two parallels, or the meridional difference of latitude,
when both places are on the same side of the equator, subtract
the meridional parts of the lesser latitude, as given by Table 3,
from the meridronal parts of the greater; the remainder will be
the meridional difference of latitude ; but if the places are on dif
ferent sides of the equator, the sum of the meridional parts will
be the meridional difference of latitude.
182. To solve the triangle CEF by the traverse tables it is only necessary to
substitute meridional difference for Lat., and difference of longitude for Dep^. Where
long distances are involved, carrying the computation beyond the limits of the
traverse table, as frequently occurs in this method, either of two means may be
adopted: the problems may be worked by trigonometrical formulae, using logarithms
or the given quantities involved may all be reduced by a common divisor until
they fall within the traverse table, and the results, when obtained, correspondingly
increased. The former method is generally preferable, especially when the distances
are quite large and accurate results are sought. The formulae for the various
conversions are as follows:
DL
Dist.
FIG. 27.
tanC =
D.Lo = mtanC; m = D.LocotC.
THE SAILINGS. 79
EXAMPLE: A ship in Lat. 42 30 N., Long. 58 51 W., sails SE. by S., 300 miles. Required the
latitude and longitude arrived at.
From Table 1: Course, SE. by S., Dist., 300; we find Lat. 249.4 S. (4 09 .4).
Latitude left, 42 3(X.O N. Merid. parts, +2806.4
DL, 4 09 .4 S.
Latitude arrived at, 38 20 .6 N. Merid. parts, -2480.4
m, 326.
By Computation.
By Inspection.
m
C
326.0
33 45
log
log tan
2. 51322
9. 82489
Enter Table 1, course 3 points;
involved exceed the limits of the
since the quantities
table, divide by 2;
DT x>
/ 217 .8
log
oViroaat /Tat "\ 1 ftl ft finA 1 1
;Dep.), 108.9; hence
2. 33811
aoreasi o l-i^ai.), luo.u, nnu o
^s Z
. -L. Q
\3 37 .8
D.Lo=217 .8or3 37 .8.
Longitude
left, 58 51 .0 W.
D.Lo,
3 37 .8 E.
Longitude arrived at, 55 13 .2 W.
EXAMPLE: A ship in Lat. 4 37 S., Long. 21 05 W., sails N. 14 W., 450 miles. Required the
latitude and longitude arrived at.
From Table 2: Course, (N.) 14 (W.), Dist., 450; we find Lat. 436.6 N. (7 16 .6).
Latitude left, 437 / .OS. Merid. parts, +275.4
DL, 7 16 . 6 N.
Latitude arrived at, 2 39 . 6 N. Merid. parts, +159.
m, 434. 4
By Computation. By Inspection,
m 434.4 log 2.63789 From Table 2: Course, 14, m (Lat.), 434.4, we find
C 14 log tan 9. 39677 D.Lo (Dep.) 108 .3 W., or 1 48 .3.
L08 . 3
48 . 3
r> T J 108 . 3 log 2.03466
-LMXK^r -
Longitude left, 21 05 . W.
D.Lo, 1 48 . 3 W.
Longitude arrived at, 22 53 . 3 W.
EXAMPLE: Required the course and distance by rhumb line from a point in Lat. 42 03 N., Long.
70 04 W., to another in Lat. 36 59 N., Long. 25 KK W.
Lat. departure, 42 03 N. Merid. pts., +2770. 1 Long, departure, 70 04 W.
Lat. destination, 36 59 N. Merid. pts., 2377. 3 Long, destination, 25 10 W.
DL
{ 5 O4 lg
\ 304 /
D.Lo 2694
m 392. 8
C (S.) 81 42 (E.)
DL 304
771,
log 3.
log 2.
392.8
43040
59417
D.
log sec. .
log 2.
.Lo
84056
48287
/44 54 \ T?
I 2694 r 4
log tan .
83623
Dist. 2106 log 3.32343
The course is therefore S. 81 42 E., and the distance is 2,106 miles. Since the
figures involved are so large, it is best to employ only the method by computation.
The formula by which the Dist. is obtained comes from Plane Sailing.
GREAT CIRCLE SAILING.
183. The shortest distance between any two points on the earth s surface is
measured by the arc of the great circle which passes through those points; and the
method of sailing in which the arc of a great circle is employed for the track of the
vessel, taking advantage of the fact that it is the shortest route possible, is denomi
nated Great Circle Sailing.
184. It frequently happens when a great circle route is laid down that it is
found to lead across the land, or to carry the vessel into a region of dangerous naviga-
80 THE SAILINGS.
tion or extreme cold which it is expedient to avoid; in such a case a certain parallel
should be fixed upon as a limit of latitude, and a route laid down such that a great
circle is followed as far as the limiting parallel, then the parallel itself, and finally
another great circle to the port of destination. Such a modification of the great
circle method is called Composite Sailing.
185. The rhumb line (art. 6, Chap. I), also called the loxodromic curve, which
cuts all the meridians at the same angle, has been largely, employed as a track by
navigators on account of the ease with which it may be laid down on a Mercator
chart. But as it is a longer line than the great circle between the same points,
intelligent navigators of the present day use the latter wherever practicable. On
the Mercator chart, however, the arc of a great circle joining two points (unless
both are on the equator or both on the same meridian) will not be projected as a
straight line, but as a curve which seems to be longer than the rhumb line; hence
the shortest route appears as a circuitous one, and this is doubtless the reason that
a wider use of the great circle has not been made.
It should be clearly understood that it is the rhumb line which is in fact the
indirect route, and that in following the great circle the vessel is always heading
for her port, exactly as if it were in sight, while on the course which is shown as a
straight line on the Mercator chart the vessel never heads for her port until at the
very end of the voyage. ^
186. The method of great circle sailing is of especial value to steamers, as such
vessels need not, in the choice of a route, have regard for the winds to the same extent
as must a sailing vessel; but even in navigating vessels under sail a knowledge of the
great circle course may prove of great value. For example, suppose a ship to be
bound from Sydney to Valparaiso; the first great circle course is SE. by S., while the
Mercator course is almost due east. The distance is 748 miles shorter by the former
route (if the great circle is followed throughout, though this would lead to a latitude
of 61 S.). With the wind at E. J S. the ship would he nearer to the Mercator course
on the starboard tack, assuming that she sailed within six points of the wind; but
if she took that tack she would be increasing her distance from the port of destination
by 4J miles in every 10 that she sailed; while on the port tack, neading one point
farther from the rhumb, the gain toward the port would be 9J miles out of every 10.
Any course between East and SSW. would be better than the Mercator course; and
if the wind were anything to the eastward of SE. by S., the ship would gain by taking
the port tack in preference to the starboard.
187. As the great circle makes a different angle with each meridian that is
crossed, it becomes necessary to make frequent changes of the ship s course; in
practice, the course is a series of chords joining the various points on the track line.
If, while endeavoring to follow a great circle, the ship is driven from it, as by
unfavorable weather, it will not serve the purpose to return to the old track at
convenience, but it is required that another great circle be laid down, joining the
actual position in which the ship finds herself with the port of destination.
188. The methods of determining the great circle course may be divided generally
into four classes; namely, by Great Circle Sailing Charts, by Computation, by the
methods of the Time Azimuth, and by Graphic Approximations.
189. GREAT CIRCLE SAILING CHARTS. Of the available methods, that by means
of charts especially constructed for the purpose is considered greatly superior to
all others.
A series of great circle sailing charts covering the navigable waters of the globe
is published by the United States Hydrographic Office. Being on the gnomonic
projection (art. 44, Chap. II), all great circles are represented as straight lines, and
it is only necessary to join any two points by such a line to represent the great circle
track between them. The courses and distance are readily obtainable by a method
explained on the charts. The track may be transferred to a chart on the Mercator
projection by plotting a number of its points by then* coordinates and joining them
with a curved line.
The navigator who contemplates the use of great circle tracks will find it of the
greatest convenience to be provided with these gnomonic charts for the regions which
his vessel is to traverse.
THE SAILINGS. 81
190. BY COMPUTATION. This method consists in determining a series of points
on the great circle by their coordinates of latitude and longitude, plotting them upon
a Mercator chart, and tracing the curve that
joins them. The first point determined is the
vertex, or point of highest latitude, even when,
as sometimes occurs, it falls without that por
tion of the great circle which joins the points
of departure and destination.
In figure 28, A represents the point of
departure; B, the point of destination; AVB,
the great circle joining them, with its vertex
at V; and P, the pole of the earth.
Let C A = PAB, the initial course ;
C B = PBA, the final course;
L A , Ly, L^the latitudes of the respective points A, V, B=(90-PA),
(90 -PV), (90-PB).
Lo^, Lo AV , Lo BV = the differences of longitude between A and B, A and V, B and V,
respectively, =APB, APV, BPV.
D = the great circle distance between A and B; and
(p = an auxiliary angle introduced for the computation.
We then have:
tan <p=cos LO^B cot LB;
cot A =cot LOAB cos (L A + 9>) cosec <p;
cot D =cps C A tan (L A -f- <p) ;
cos Ly = sin C A cos L A ;
cot Lo AV = tan C A sin L A .
By these formulae are determined the initial course and the total distance by
great circle; also the latitude of the vertex and its longitude with respect to A. By
interchanging the subscript letters A and B throughout, we should obtain the final
course, and the longitude of the vertex with respect to B; also the same total distance
and latitude of the vertex as before.
In performing this computation, strict regard must be had to the signs of the
quantities. If the points of departure and destination are in different latitudes, the
latitude of one of these points must be regarded as negative with respect to the other,
and they must be marked with opposite signs. Should Lo AV or Lo BV assume a
negative value, it indicates that the vertex does not lie between A and B, and is to
be laid off accordingly.
To find other points of the great circle, M, N, etc., let their latitudes be repre
sented by LM, LN, etc., and their longitudes from the vertex by Lo^, LOVK, e tc.;
then
tan LH = tan Ly cos Lo^; or, cos Lo VM = tan LM cot L^;
tan L^ = tan Ly cos Lo^; or, cos Lo VN = tan L^ cot Ly;
and so on. By these formulae intervals of longitude from the vertex of 5, 10, -or
any amount, may be assumed, and the corresponding latitudes deduced; or any
latitude may be assumed and its corresponding interval of longitude from the
vertex found. Two positions will result from each solution, and the appropriate
ones may be chosen by keeping in mind the signs involved.
EXAMPLE: Given two places, one in Lat. 40 N., Long. 70 W., the other in Lat. 30 S., Long. 10
W., find the great circle distance between them; also the initial course, and the longitude of equator
crossing.
L A =+40; L B =-30; Lo AB =60.
Lo AB 60 cos 9. 69897.. cot 9.76144
LB - 30 cot (-) .23856
L A +40 cos 9. 88425 sin 9.80807
g> - 40 54 tan ( -) 9. 93753.. cosec (-) .18393
(L A +<P) - 54 cos 9. 99995 tan (-) 8. 19616
C A 131 24 orS.4836 / E cot ( ) 9. 94532 cos (-) 9. 82041 siii 9.87513 tan (-) .05472
D 89 24 or 5,364 miles cot 8.01657
LT + 54 56 cos 9. 75938
Lo AT - 53 54 . ., cot (-) 9.86279
82
THE SAILINGS.
The initial course is therefore S. 48 36 E., and the distance 5,364 nautical
miles. (It may be found that the course by rhumb line is S. 38 45 E. and the
distance 5,386 miles.) The vertex of the great circle is in Lat. 54 56 N., and is
53 54 in longitude from the point A, in a direction away from B; hence it is in
Long. 123 54 W. To find the longitude of equator crossing let L M = 0; then in
the equation,
cos LOVM = tan L M cot L v ,
since tan L M equals zero, cos Lo VM also equals zero, or the longitude interval from
the vertex is 90, which is evident from the properties of the great circle: therefore
the longitude of equator crossing is 123 54 W. 90 = 33 54 W.
191. BY TIME AZIMUTH METHODS. A convenient method of obtaining the initial
and final couises in great circle sailing is afforded by the tables and graphic methods
which are prepared for the solution of the Time Azimuth problem (art. 352, Chap.
XIV). It will be found by comparison that if the latitude of the point of departure
be substituted for the latitude of the observer in that problem, the latitude of desti
nation for the declination of the celestial body, and the longitude interval for the
hour angle, the solution for the initial course will coincide with that for the azimuth;
by interchanging the latitudes of the points of departure and destination the final
course will be similarly obtained. Advantage may thus be taken of the various
methods provided for facilitating the determination of the azimuth to ascertain
the great circle courses from one point to another.
192. BY GRAPHIC APPROXIMATIONS. Of the numerous methods that fall
within this class only two need be given.
193. By the use of a Terrestrial Globe the two given points between which the
great circle track is required may be joined by the shortest line between them, either by
means of a piece of thread or by moving the globe until they are brought to the fixed
horizon which is usually provided; the coordinates of the various points of the track
are then transferred to the chart. The number of minutes of arc, as measured on
the scale of the horizon between the points, equals the number of miles of distance;
if there be no Horizon, the measure may be made by a thread along the equator or a
meridian.
194. The Method of Professor Airy consists in drawing on the chart a rhumb
line joining the two points, and erecting at its middle point a perpendicular; the
following table should then be entered with the middle latitude as an argument, and
the " corresponding parallel" of latitude taken out (noting whether it is the same
or opposite in name to the middle latitude) ; where this parallel is intersected by the
perpendicular that was drawn will be the center from which may be swept an arc
approximately representing the great circle between the two points.
Middle lati
tude.
Correspond
ing parallel.
Name.
Middle lati
tude.
Correspond
ing parallel.
Name.
O
e /
/
20
81 13
Opposite.
52
11 33
Opposite.
22
78 16
Do.
54
6 24
Do.
24
74 59
Do.
56
1 13
Do.
26
71 26
Do.
58
4 00
Same.
28
67 38
Do.
60
9 15
Do.
30
63 37
Do.
62
14 32
Do.
32
59 25
Do.
64
19 50
Do.
34
55 05
Do.
66
25 09
Do.
36
50 36
Do.
68
30 30
Do.
38
46 00
Do.
70
35 52
Do.
40
41 18
Do.
72
41 14
Do.
42
36 31
Do.
74
46 37
Do.
44
31 38
Do.
76
52 01
Do.
46
26 42
Do.
78
57 25
Do.
48
21 42
Do.
. 80
62 51
Do.
50
16 39
Do.
THE SAILINGS. 83
COMPOSITE SAILING.
195. It has already been stated that when, for any reason, it is impracticable
or unadvisable to follow the great circle track to its highest latitude, a limiting parallel
is chosen and the route modified accordingly. This method is denominated Composite
Sailing.
196. The shortest track between points where a fixed latitude is not exceeded
is made up as follows :
1. A great circle through the point of departure tangent to the limiting parallel.
2. A course along the parallel.
3. A great circle through the point of destination tangent to the limitingparallel.
The composite track may be determined by Great Circle Sailing Chart, by
Computation, or by Graphic Approximation.
197. On a Great Circle Sailing Chart, draw lines from the points of departure
and destination, respectively, tangent to the limiting parallel; transfer these great
circles to a Mercator chart in the usual manner, by the coordinates of several points,
including in each case the point of tangency to the parallel. Follow the first great
circle to the parallel; then follow the parallel; then the second great circle.
Determine great circle courses and distances from the gnomonic chart as thereon
described; determine the distance along the parallel by Parallel Sailing.
198. By computation, the problem consists in finding the great circles which
pass, respectively, through the points of departure and destination and have their
vertices in the latitude of the limiting parallel. Resuming the designation of terms
already employed (art. 190), we have:
cos Lo VA = tan L A cot L v ;
cos Lo VB = tan L B cot L v ;
where Lo VA and Lo VB represent the distances in longitude from A and from B to the
respective points of tangency; other features of each of the great circles may be
determined in the usual manner.
EXAMPLE: A vessel in Lat. 30 S., Long. 18 W., is bound to a point in Lat. 39 S., Long. 145 E.,
and it is decided not to go south of the parallel of 55 S. Find the longitude of reaching that parallel
and the longitude at which it should be left.
L^=30S.; L B = 39 S.; L V = 55S.
Lo A =lSW.; LOB = 145 E.
L A 30 tan 9. 76144 L B 39 tan 9. 90837
L v 55 cot 9.84523 L v 55 cot 9.84523
Low 66 09 E. cos 9. 60667 Lo VB 55 27 W. cos 9. 75360
Lo A 18 00 W. Lo B 145 00 E.
Lo v 48 09 E. Lo v 89 33 E.
199. A graphic approximation to the composite track may be obtained by drawing
a straight line between the given points on a Mercator chart and erecting at its middle
point a perpendicular, which should be extended until it intersects the limiting
parallel. Then through this intersection and the two points describe the arc of a
circle, and this will approximate to the shortest distance within the assigned limit
of latitude.
200. A terrestrial globe may be employed for the determination of the composite
track; the method of its use will suggest itself.
201. Another approximation is obtained by joining the two points with a single
great circle, and following this to its intersection with the limiting parallel; thence
sailing along the parallel until the great ^ circle is again intersected; then resuming
the circle and following it to the destination.
CHAPTER VI.
DEAD EECKONINO.
202. Dead Reckoning is the process by which the position of a ship at any instant
is found by applying to the last well-determined position the run that has since been
made, using for the purpose the ship s course and the distance indicated by the log.
203. Positions by dead reckoning, also spoken of as positions by account, differ
from those determined by bearings of terrestrial objects or by observations of celestial
bodies in being less exact, as the correctness of dead reckoning depends upon the
accuracy of the estimate of the run, and this is always liable to be at fault to a greater
or less extent. The course made good by a ship may differ from that which it is
believed that she is making good, by reason of imperfect steering, improper allowance
for compass error and leeway, and the effects of unknown currents; the allowed
distance over the ground may be in error on account of inaccurate logging and
unknown currents.
Notwithstanding its recognized defects as compared with the more exact methods,
the dead reckoning is an invaluable aid to the mariner. It affords him a means of
plotting the position of the ship at any desired time between astronomical deter
minations; it also gives him an approximate position at the moment of taking
astronomical observations which is a great convenience in working up those observa
tions; and finally it affords the only available means of determining the location of
a vessel at sea during those periods (which may continue for several days together)
when the weather is such as to render the observation of celestial bodies an impos
sibility.
204. TAKING DEPARTURE. Before losing sight of the land, and preferably
while objects remain in good view, it is the duty of the navigator to take a departure;
this consists in fixing the position of the ship by the best means available (Chap. IV),
and using this position as the origin for dead reckoning. ^ There are two methods of
reckoning the departure. The first and simpler consists in taking from the chart the
latitude and longitude of the position found, and applying the future run thereto.
The other requires that the bearing and distance of an object of known latitude and
longitude be found; the position of the object then forms the basis of the reckoning,
and the reversed direction of the bearing, with the distance, forms the first course
and distance ; thus it may be considered that the ship starts from the position of the
object and sails to the position where the bearing was taken; the correction for
deviation in such a case should be that due to the heading of the ship when the bearing
was taken. Each time that a new position is determined it is used as a new departure
for the dead reckoning.
This meaning of the term departure should not be confounded with the other,
which refers to tlie distance run toward east or west.
205. METHODS. The working of dead reckoning merely involves an application
of the methods of Traverse Sailing (art. 172) and Middle Latitude Sailing (art. 175),
as explained in Chapter V.
The various compass courses are set down in a column, and abreast each are
written the errors by reason of which the course steered by compass differs from the
true course made good over the ground; thence the true course made good is deter
mined and recorded; next, the distance is written in, and afterwards, by means of
Tables 1 or 2 (according as the courses are expressed in quarter points or degrees) , the
difference of latitude and departure are found, separate columns being kept for
distances to the north, south, east, and west.
When the position of the ship at any moment is required, add up all the differ
ences of latitude and departure, and write in the column of the greater the difference
between the northing and southing, and the easting and westing. Apply the differ
ence of latitude to the latitude of the last determined position, which will give the
84
DEAD RECKONING.
85
latitude by D. R., and from which may be found the middle latitude; with the
middle latitude find the difference of longitude corresponding to the departure, apply
this to the longitude of last position, and the result will be the longitude by D. R.
The employment of the tabular form will be found to facilitate the work and
guard against errors. It will be a convenience to include in that form columns
showing the hour, together with the reading of the patent log (if used) each time
that the course is changed or the dead reckoning worked up.
The employment of minutes and tenths in dead reckoning rather than minutes
and seconds is recommended.
EXAMPLE: A vessel under sail heading NE. f E. (on which course deviation is
J pt. Easterly) takes departure from Cape Henry lighthouse (see Appendix IV for
position), bearing SSW. J W. per compass, distant 1.4 miles. She then sails on a
series of courses, with errors and distances as indicated below; wind about SE. by E.
Required the position by dead reckoning; also the course and distance made good by
dead reckoning.
Comp. course.
Var.
Dev.
Leeway.
Error.
True course.
Dist.
N.
S.
E.
W.
D. Lo.
NNE. * E.
tw
iE.
iW.
NNE. iE.
1.4
1.3
0.6
NE. | E.
S. by W.
rWi
r w.
r E.
iW.
iW.
NE. iE.
S. f W.
27.6
31.5
18.5
31.2
20.5
4.6
ENE.
W
i E.
r w.
i\v.
NE.byE.iE.
14.2
7.3
12.2
S.iE.
NE.iN.
W.
W.
r|.
S.iE.
NE. byN.
11.0
87.0
72.3
11.0
0.5
48.3
99.4
42. 2
82.1
4.6
Made good,
NE. | E.
96.5
57.2
77.5
97.0
Point of departure,
Bun,
By D. R.
Latitude.
36 55 . 6 N.
57.2 N.
37 52.8 N.
Mid. L., 37<
Longitude.
76 00 . 5 W.
1 37. OE.
74 23. 5 W.
EXAMPLE: A steamer s position by observation at noon, patent log reading 27.3, is Lat. 49 15 N.,
Long. 7 32 W. Thence she steers 262 (per compass), the total compass error on that course being
20 W., until 12.30, at which time, patent log reading 33.9, the course is changed to 260 (p. c.), same
error. At 4.12, patent log 80.5, sights are taken from which it is found that the true longitude is 8 46 W.,
and the compass error 19 W. At 6.15, patent log reading 6.1, a eight is taken from which it is found
that the true latitude is 48 34 30" N. At 8 p. m. the patent log reads 27.5. Required the positions by
D. B. at each sight and at 8 o clock.
Time.
Comp. course.
Error.
True course.
Pat. Log.
Dist.
S.
W.
D. Lo.
Noon.
g
27.3
12.30
262
20 W.
242
33.9
6.6
3.1
5.8
4.12
260
20 W.
240
80.5
46.6
23.3
40.3
26.4
46.1
70.3
6.15
260
19 W.
241
6.1
25.6
12.4
22.4
34.1
8.00
260
19 W.
241
27.5
21.4
10.4
18.7
27.9
Latitude.
Byobs.atnoon, 49 15 .0 N.
Run to 4.12 sight, 26 .4 S.
Mid. L., 49
By D. R. at 4.12 sight, 48 48 .6 N.
By obs. at 4.12 sight,
Run to 6.15 sight, 12 .4 S.
By D. R. at 6.15 sight, 48 36 .2 N.
Longitude.
7 32 .0 W.
1 10 .3 W.
8 42 .3 W.
S 46 .0 W.
Mid. L., 49 34 .1 W.
By obs. at 6.15 sight,
Run to 8 p. m.,
48 34 .5 N.
10 .4 S.
Mid. L., 4S<
9 20 .1 W.
27 .9 W.
By D. R. at 8 p. m., 48 24 .1 N.
9 48 .0 W.
86
DEAD RECKONING.
206. ALLOWANCE FOR CURRENT. When a vessel is sailing in a known current
whose strength may be estimated with a fair degree of accuracy, a more correct
position may be arrived at by regarding the set and drift of the current as a course and
distance to be regularly taken account of in the dead reckoning.
EXAMPLE: A vessel in the Gulf Stream at a point where the current is estimated to set 48 at the
rate of 1.8 miles an hour, sails 183 (true), making 9.5 knots an hour through the water for 3 h 30 m . Middle
latitude 35. Required the course and distance made good.
True course.
Dist.
N.
S.
E.
w.
D. Lo.
Run
Current
Made good
183
48
174
33.3
6.3
29.3
4.2
33.3
4.7
1.7
3.6
29.1
3.0
207. FINDING THE CURRENT. It is usual, upon obtaining a good position by
observation (as the navigator usually does at noon), to compare that position with
the one obtained by dead reckoning, and to attribute such discrepancy as may be
found to the effects of current. It has already been pointed out that other
causes than the motion of the water tend to make the dead reckoning inaccurate,
so that it must not be assumed that currents proper are thus determined with com
plete correctness.
Current is said to have set and drift, referring respectively to the direction toward
which it is flowing and the velocity with which it moves.
It is evident that, in calculating current by the method of comparing positions
by observation with those by account, the navigator must limit himself to the periods
during which the dead reckoning has been brought forward independently, without
receiving any corrections due to new points of departure. In case it is desired to
find the current covering a period during which fresh departures have been used,
as from noon to noon, find the algebraical sums of all the differences of latitude and
longitude from the table, and apply these to the latitude and longitude of original
departure that of the preceding noon; this gives the position from the ship s run
proper, and the difference between this and the position by observation gives the set
and drift for the twenty-four hours ; if an allowance has been made for current, as
explained in the preceding article, that must be omitted in bringing up the position
which is to take account of the run only.
208. DAY S KUN. It is usual to calculate, each day at noon, the ship s total run
for the preceding twenty-four hours. Having the positions at noon of each day, the
course and distance between them is found as explained in article 175, Chapter V.
The position by observation is used in each case, ii such has been found; otherwise,
the position by dead reckoning.
t
EXAMPLE: At noon, January 22, the position of a vessel by observation was Lat. 35 10 7 N., Long.
134 Ol x W. During the next 24 hours, the run by account was 60.1 miles north and 153.2 miles east.
At noon, January 23, the position by observation was Lat. 36 03 N., Long. 131 14 W. Required
the position by D. R. at the latter time; also the run and current for the 24 hours.
By obs., noon, 22d,
Run,
Latitude.
35 10<ON.
1 00 .1 N.
. By D. R., noon, 23d, 36 10 .1 N.
Mid. L., 36
Dep., 153.2 E.
D.Lo., 189.4 E.
Longitude.
134 Ol .O W.
3 09 .4 E.
130 51 .6 W.
By obs., noon, 23d ? 36 03 .0 N. D.Lo., 22.4 W. 131 14 .0 W.
Current,
p.Lo., 22.4 W.j 131 14 .0 W.
JDep., 18.1 W.J 22.4 W.
6 .9 S. Dep., 18.
Current for 24 hours, 6.9 S., 18.1 W.=249, 19.4 miles.
Current per hour, 249, 0.8 mile.
Latitude.
Longitude.
By obs.,
By obs.,
noon,
noon,
23d
22d
36
35
03 .
10 .0
N. 1
N.
Mid.
D.Lo
L., 36
.,167. OB.
131
134
14
01
.0
.0
w.
w.
Run
i
53 .0
N. j
Dep., 135.1
2
47
.0
E.
Run for 24 hours, 53.0 N., 135.1
E.=6S,
146 miles.
CHAPTER VII.
DEFINITIONS KELATING- TO NAUTICAL ASTEONOMY,
209. Nautical Astronomy, or Celo- Navigation, has been defined (art. 3, Chap. I)
as that branch of the science of Navigation in which the position of a ship is deter
mined by the aid of celestial objects the sun, moon, planets, or stars.
210. THE CELESTIAL SPHERE. An observer upon the surface of the earth
appears to view the heavenly bodies as if they were situated upon the surface of a
vast hollow sphere, of which his eye is the center. In reality we know that this
apparent vault has no existence, and that we can determine only the relative directions
of the heavenly bodies not their distances from each other or from the observer.
But by adopting an imaginary spherical surface of an infinite radius, the eye of the
observer being at the center, the places of the heavenly bodies can be projected upon
this Celestial Sphere, or Celestial Concave, at points where the lines joining them with
the center intersect the surface of the sphere. Since, however, the center of the earth
should be the point from which all angular distances are measured, the observer,
by transferring himself there, will find projected on the celestial sphere, not only
the heavenly bodies, but the imaginary points and circles of the earth s surface.
The actual position of the observer on the surface will be projected in a point called
the zenith; the meridians, equator, and all other lines and points may also be projected.
211. An observer on the earth s surface is constantly changing his position with
relation to the celestial bodies projected on the sphere, thus giving to the latter an
apparent motion. This is due to three causes: First, the diurnal motion of the earth,
arising from its rotation upon its axis; second, the annual motion of the earth,
arising from its motion about the sun in its orbit; and third, the actual motion of
certain of the celestial bodies themselves. The changes produced by the diurnal
motion are different for observers at different points upon the earth, and therefore
depend upon the latitude and longitude of the observer. But the changes arising
from the other causes named are independent of the observer s position, and may
therefore be considered at any instant in their relation to the center of the earth.
To this end the elements necessary for any calculation are tabulated in the Nautical
Almanac from data based upon laws which have been found by long series of observa
tions to govern the actual and apparent motion of the various bodies.
212. The Zenith of an observer on the earth s surface is the point of the celestial
sphere vertically overhead. The Nadir is the point vertically beneath.
213. The Celestial Horizon is the great circle of the celestial sphere formed by
passing a plane through the center of the earth at right angles to the line which joins
that point with the zenith of the observer. The celestial horizon differs somewhat
from the Visible Horizon, which is that line appearing to an observer at sea to mark
the intersection of earth and sky. This difference arises from two causes: First, the
eye of the observer is always elevated above the sea level, thus permitting him a
range of vision exceeding 90 from the zenith; and second, the observer s position
is on the surface instead of at the center of the earth. These causes give rise, respec
tively, to dip of the horizon and parallax, which will be explained later (Chap. X).
214. In figure 29 the celestial sphere is considered to be projected upon the
celestial horizon, represented by NESW. ; the zenith of the observer is projected at
Z, and that pole of the earth which is elevated above the horizon, assumed for illus
tration to be the north pole, appears at P, the Elevated Pole of the celestial Sphere.
The other pole is not shown in the figure.
87
88
DEFINITIONS RELATING TO NAUTICAL ASTRONOMY.
215. The Equinoctial, or Celestial Equator, is the great circle formed by extending
the plane of the earth s equator until it intersects the celestial sphere. It is shown
in the figure in the line EQW. The equinoctial intersects the horizon in E and W,
its east and west points.
216. Hour Circles, Declination Circles, or Celestial Meridians are great circles
of the celestial sphere passing through the poles; they are therefore secondary to
the equinoctial, and may be formed by extending the planes of the respective terres
trial meridians until they intersect the celestial sphere. In the figure, PB, PS, PB ,
are hour circles, and that one, PS, which contains the zenith and is therefore formed
by the extension of the terrestrial meridian of the observer, intersects the horizon in
N and S, its north and south points.
217. Vertical Circles, or Circles of Altitude, are great circles of the celestial
sphere which pass through the zenith and nadir; they are therefore secondary to
the horizon. In the figure, ZH, WZE, NZS, are projections of such circles, which
being at right angles to the plane of projection, appear as straight lines. The vertical
circle NZS, which passes through the poles, coincides with the meridian of the
observer. The vertical circle WZE, whose plane is at right angles to that of the
meridian, intersects the horizon in its eastern and western points, and, therefore,
at the points of intersection of the equinoc
tial ; this circle is distinguished as the Prime
Vertical.
218. The Declination of any point in
the celestial sphere is its angular distance
from the equinoctial, measured upon the
hour or declination circle which passes
through that point; it is designated as
North or South according to the direction
of the point from the equinoctial ; it is cus
tomary to regard north decimations as
positive ( + ), and south declinations as nega
tive ( ). In the figure, DM is the declina
tion of the point M. Declination upon the
celestial sphere corresponds with latitude
upon the earth.
219. The Polar Distance of any point
is its angular distance from the pole (gen
erally, the elevated pole of an observer),
measured upon the hour or declination circle
passing through the point; it must therefore
equal 90 minus the declination, if measured from the pole of the same name as the
declination, or 90 plus the declination, if measured from the pole of opposite name.
The polar distance of the point M from the elevated pole P is rM.
220. The Altitude of any point in the celestial sphere is its angular distance
from the horizon, measured upon the vertical circle passing through the point; it
is regarded as positive when the body is on the same side of the horizon as the zenith.
The altitude of the point M is HM.
221. The Zenith Distance of any point is its angular distance from the zenith,
measured upon the vertical circle passing through the point; the zenith distance
of any point which is above the horizon of an observer must therefore equal 90
minus tne altitude. The zenith distance of M, in the figure, is ZM.
222. The Hour Angle of any point is the angle at the pole between tl^e meridian
of the observer and the hour circle passing through that point; it may also be regarded
as the arc of the equinoctial intercepted between those circles. It is measured
toward the west as a positive direction through the twenty-four hours, or 360 degrees,
which constitute the interval between the successive returns to the meridian, due
to the diurnal rotation of the earth, of any point in the celestial sphere. The hour
angle of M is the angle QPD, or the arc QD.
223. The Azimuth of a point in the celestial sphere is the angle at the zenith
between the meridian of the observer and the vertical circle passing through the
FIG. 29.
DEFINITIONS RELATING TO NAUTICAL ASTKONOMY. 89
point; it may also be regarded as the arc of the horizon intercepted between those
circles. It is measured from either the north or the south point of the horizon
(usually that one of the same name as the elevated pole) to the east or west through
180, and is named accordingly; as, N. 60 W., or S. 120 W. The azimuth of M is
the angle NZH, or the arc sH, from the north point, or the angle SZH, or the arc
SH, from the south point of the horizon.
224. The Amplitude of a point is the angle at the zenith between the prime
vertical and the vertical circle of the point; it is measured from the east or the west
point of the horizon through 90, as W. 30 N. It is closely allied with the azimuth
and may always be deduced therefrom. In the figure, the amplitude of H is the
angle WZH, or the arc WH. The amplitude is only used with reference to points
in the horizon.
225. The Ecliptic is the great circle representing the path in which, by reason
of the annual revolution of the earth, the sun appears to move in the celestial sphere;
the plane of the ecliptic is inclined to that of the equinoctial at an angle of 23^27^ ,
and this inclination is called the obliquity of the ecliptic. The ecliptic is represented
by the great circle CVT.
226. The Equinoxes are those points at which the ecliptic and the equinoctial
intersect, and wnen the sun occupies either of these positions the days and nights
are of equal length throughout the earth. The Vernal Equinox is that one at wnich
the sun appears to an observer on the earth when passing from southern to northern
decimation, and the Autumnal Equinox that one at which it appears when passing
from northern to southern declination. The Vernal Equinox is also designated as
the First Point of Aries, and is used as an origin for reckoning right ascension; it is
indicated in the figure at V.
227. The Solstitial Points, or Solstices, are points of the ecliptic at a distance
of 90 from the equinoxes, at which the sun attains its highest declination in each
hemisphere. They are called respectively the Summer and the Winter Solstice,
according to the season in which the sun appears to pass these points in its path.
The Summer Solstice is inolicated in the figure at U.
228. The Eight Ascension of a point is the angle at the pole between the hour
circle of the point and that of the First Point of Aries; it may also be regarded as
the arc of the equinoctial intercepted between those circles. It is measured from
the First Point of Aries to the eastward as a positive direction, through twenty-four
hours or 360 degrees. The right ascension of the point M is VD .
229. Celestial Latitude is measured to the north or south of the ecliptic upon
great circles secondary thereto. Celestial Longitude is measured upon the ecliptic
From the First Point of Aries as an origin, being regarded as positive to the eastward
throughout 360.
230. COORDINATES. In order to define the position of a point in space, a system
of lines, angles, or planes, or a combination of these, is used to refer it to some fixed
line or plane adopted as the primitive; and the lines,
angles, or planes by which it is thus referred are called H
coordinates.
231. In figure 30 is shown a system of rectilinear
coordinates for a plane. A fixed line FE is chosen, and D
in it a definite point C, as the origin. Then the posi
tion of a point A is defined by CB = x, the distance F C x E
from the origin, C, to the foot of a perpendicular let " B
fall from A on FE; and by AB=7/, the length of the
perpendicular. The distance x is called the abscissa I
ana y the ordinate. Assuming two intersecting right FIG. so.
lines FE and HI as standard lines of reference, the
location of the point A is defined by regarding the distances measured to the right
hand of HI and above FE as positive; those to the left hand of HI and below FE
as negative.
An exemplification of this system is found in the chart, on which FE is represented
by the equator, HI by the prime meridian; the coordinates x and y being the longitude
and latitude of the point A.
232. The great circle is to the sphere what the straight line is to the plane;
hence, in order to define the position of a point on the surface of a sphere, some great
90 DEFINITIONS RELATING TO NAUTICAL ASTRONOMY.
circle must be selected as the primary, and some particular point of it as the origin.
Thus, in figure 31, which represents the case of a sphere, some fixed great circle,
CBQ, is selected as the axis and called the primary; and a point C is chosen as the
origin. Then to define the position of any point A, the ab
scissa x equals the distance from C to the point B, where
the secondary great circle through A intersects the primary;
the ordinate y equals the distance of A from the primary
measuied on the secondary that is, x = CE and y = AB C
233. In the case of the earth, the primary selected is
the equator (its plane being perpendicular to the earth s
axis), and upon this are measured the abscissae, while upon
the secondaries to it are measured the ordinates of all
points on the earth s surface. The initial point for refer
ence on the equator is determined by the prime meridian
FIG. si. chosen, West longitudes and North latitudes being called
positive, East longitudes and South latitudes, negative.
234:. In the case of the celestial sphere, there are four systems of coordinates
in use for defining the position of any point; these vary according to the circle
adopted as the primary and the point used as an origin. They are as follows:
1. Altitude and azimuth.
2. Declination and hour angle.
3. Declination and right ascension.
4. Celestial latitude and longitude.
235. In the system of Altitude and Azimuth, the primary circle is the celestial
horizon, the secondaries to which are the vertical circles, or circles of altitude. The
horizon is intersected by the celestial meridian in its northern and southern points,
of which one usually that adjacent to the elevated pole is selected as an origin
for reckoning coordinates. The azimuth indicates in which vertical circle the point
to be defined is found, and the altitude gives the position of the point in that circle.
In figure 29 the point M is located, according to this system, by its azimuth NH
and altitude HM.
236. In the system of Declination and Hour Angle, the primary circle is the
equinoctial, the secondaries to which are the circles of declination, or hour circles.
The point of origin is that point of intersection of the equinoctial and celestial
meridian which is above the horizon. The hour angle indicates in which declina
tion circle the point to be defined is found, and the declination gives the position
of the point in that circle. In figure 29 the point M is located, according to this
system, by its hour angle QD and declination DM.
237. In the system of Declination and Right Ascension, the primary and seconda
ries are the same as in the system just described, but the point of origin differs, being
assumed to be at the First Point of Aries, or vernal equinox. The right ascension
indicates in which declination circle the point to be defined may be found, and the
decimation gives the position in that circle. In figure 29 the point M is located by
VD , the right ascension, and D M , the declination. It should^be noted that this
system differs from the preceding in that the position of a point is herein referred to
a fixed point in the celestial sphere and is independent of the zenith of the observer
as well as of the position of the earth in its diurnal motion, while, in the system of
declination and hour angle, both of these are factors in determining the coordinates.
238. In the system of Celestial Latitude and Longitude, the primary circle is the
ecliptic; the point of origin, the First Point of Aries. The method of reckoning by
this system, which is of only slight importance in Nautical Astronomy, will appear
from the definitions of celestial latitude and longitude already given (art. 229).
CHAPTER VIII.
INSTEUMENTS EMPLOYED IN NAUTICAL ASTEONOMY.
THE SEXTANT.
239. The sextant is an instrument for measuring the angle between two objects
by bringing into coincidence at the eye of the observer rays of light received directly
from the one and by reflection from the other, the measure being afforded by the
inclination of the reflecting surf aces. By reason of its small dimensions, its accuracy,
and, above all, the fact that it does not require a, permanent or a stable mounting
but is available for use under the conditions existing on shipboard, it is a most
important instrument for the purposes of the navigator. While the sextant is not
capable of the same degree of accuracy as fixed instruments, its measurements are
sufficiently exact for navigation.
240. DESCRIPTION. A usual form of the sextant is represented in figure 32.
The frame is of brass or some similar alloy. The graduated arc, AA, generally of
silver, is marked in appro
priate divisions; in the nner ii M
sextants, each division rep
resents 10 , and the vernier
affords a means of reading
to 10". A wooden handle,
H, is provided for holding
the instrument. The index
mirror, M, and horizon, mir
ror, m, are of plate glass,
and are silvered, though the
upper half of the horizon
glass is left plain to allow
direct rays to pass through
unobstructed. To give
greater distinctness to the
images, a small telescope, E,
is placed in the line of sight ;
it is supported in a ring, K,
which can be moved by a
screw in a direction at right
angles to the plane of the sex
tant, thus shifting the axis
of the telescope, and therefore the plane of reflection; this plane, however, always
remains parallel to that of the instrument, the motion of the telescope being intended
merely to regulate the relative brightness of the direct and reflected image. In the
ring, K, are small screws for the purpose of adjusting the telescope by making its axis
parallel with the plane of the sextant. The vernier is carried on the end of an index
bar pivoted beneath the index mirror, M, and thus travels along the graduated scale,
affording a measure for any change of inclination of the index mirror; a reading glass,
R, attached to the index bar and turning upon a pivot, S, facilitates the reading of
vernier and scale. The index mirror, M, is attached to the head of the index bar, with
its surf ace perpendicular to the plane of the instrument; an adjusting screw is fitted
at the back to permit of adjustment to the perpendicular plane. The fixed glass m,
half silvered and half plain, is called the Jwrizon glass, as it is through this that the
FIG. 32.
92 INSTRUMENTS EMPLOYED IN NAUTICAL ASTRONOMY.
horizon is observed in measuring altitudes of celestial bodies; it is provided with
screws, by which its perpendicularity to the plane of the instrument may be
adjusted. At P and Q are colored glasses of different shades, which may be used
separately or in combination to protect the eye from the intense light of the sun.
In order to observe with accuracy and make the images come precisely in contact, a
tangent screw, B, is fixed to the index, by means of which the latter may be moved
with greater precision than by hand ; but this screw does not act until the index is
fixed by the screw "C at the back of the sextant; when the index is to be moved any
considerable amount, the screw C is loosened; when it is brought near to its
required position the screw must be tightened, and the index may then be moved
gradually by the tangent screw.
Besides the telescope, E, the instrument is usually provided with an inverting
telescope, I, and a tube without glasses, F; also, with a cap carrying colored glasses,
which may be put on the eye end of the telescope, thus dispensing with the necessity
for the use of the colored shades, P and Q, and eliminating any possible errors which
might arise from nonparallelism of their surfaces.
The latest type of sextant furnished to the United States Navy is fitted with an
endless tangent screw which carries a micrometer drum from which the seconds of
arc are read. By pressure of the thumb the tangent screw is released and the index
bar may be moved to any position on the arc by hand, where the tangent screw is
again thrown into gear by releasing the pressure of the thumb. The endless tangent
screw is accomplished by cutting the edge of the arc with the worm teeth into which
the tangent screw gears. At night the reading of this sextant is facilitated by a
small electric light carried on it and supplied by a battery contained in the handle.
241. The vernier is an attachment for facilitating the exact reading of the scale
of a sextant, by which aliquot parts of the smallest divisions of the graduated scale
are measured. The principle of the sextant vernier is identical with that of the
barometer vernier, a complete description of which will be found in article 52, Chapter
II. The arc of a sextant is usually divided into 120 or more parts, each division
representing 1; each of these degree divisions is further subdivided to an extent
dependent upon the accuracy of reading of which the sextant is capable. In the
instruments tor finer work, the divisions of the scale correspond to 10 each, and the
vernier covers a length corresponding to 59 such divisions, which is subdivided into
60 parts, thus permitting a reading of 10"; all sextants, however, are not so closely
graduated.
Whatever the limits of subdivision, all sextants are fitted with verniers which
contain one more division than the length of scale covered, and in which, therefore,
scale-readings and vernier-readings increase in the same direction toward the left
hand. To read any sextant, it is merely
necessary to observe the scale division next
F below, or to the right of, the zero of the
..- ** vernier, and to add thereto the angle cor-
, x responding to that division of the vernier
,,- scale which is most nearly in exact coin
cidence with a division of the instrument
1 scale.
242. OPTICAL PRINCIPLE. When a
ray of .light is reflected from a plane surface,
the angle of incidence is equal to the angle
^j) of reflection. From this it may be proved
Flo 33 that when a ray of light undergoes two
reflections in the same plane the angle be
tween its first and its last direction is equal to twice the inclination of the reflecting
surfaces. Upon this fact the construction of the sextant is based.
In figure 33, let B and C represent respectively the index mirror and horizon
mirror of a sextant; draw EF perpendicular to B, and CF perpendicular to C; then
the angle CFB represents the inclination of the two mirrors. Suppose a ray to pro
ceed from A and undergo reflection at B and at C, its last direction being CD; then
ADC is the angle between its first and last directions, and we desire to prove that
ADC = 2 CFB.
INSTRUMENTS EMPLOYED IN NAUTICAL ASTRONOMY. 93
From the equality of the angles of incidence and reflection:
ABE = EEC, and ABC = 2 EEC;
BCF = FCD, and BCD = 2 BCF.
From Geometry:
ADC = ABC - BCD = 2 (EEC - BCF) = 2 CFB,
which is the relation that was to be proved.
243. In the sextant, since the index mirror is immovably attached to the index
arm, which also carries the vernier, it follows that no change can occur in the inclina
tion between the index mirror and the horizon mirror, excepting such as is registered
by the travel of the vernier upon the scale.
If, when the index mirror is so placed that it is nearly parallel with the horizon
mirror, an observer direct the telescope toward some well-defined object, there will
be seen in the field of view two separate images of the object; and if the inclination
of the index mirror be slightly changed by moving the index bar, it will be seen that
while one of the images remains fixed the^other moves. The fixed image is the direct
one seen through the unsilvered part of the horizon glass, while the movable image
is due to rays reflected by the index and horizon mirrors. When the two images
coincide these mirrors must be parallel (assuming that the object is sufficiently distant
to disregard the space which separates the mirrors; in this position of the index
mirror the vernier indicates the true zero of the scale. If, however, instead of
observing a single object, the instrument is so placed that the direct ray from one
object appears in coincidence with the reflected ray of a second object, then the true
angle between the objects will be twice the angle of inclination between the mirrors,
or twice the angle measured by the vernier from the true zero of the scale. To avoid
the necessity of doubling the angle on the scale, the latter is so marked that each
half degree appears as a whole degree, whence its indications give the whole angle
directly.
244. ADJUSTMENTS OF THE SEXTANT. The theory of the sextant requires that,
for accurate indications, the following conditions be fulfilled:
(a) The two surfaces of each mirror and shade glass must be parallel planes.
(6) The graduated arc or limb must be a plane, and its graduations, as well as
those of the vernier, must be exact.
(c) The axis must be at the center of the limb, and perpendicular to the plane
thereof.
(d) The index and horizon glasses must be perpendicular, and the line of sight
parallel to the plane of the limb.
Of these, only the last named ordinarily require the attention of the navigator
who is to make use of the sextant ; the others, which may be called the permanent
adjustments, should be made before the instrument leaves the hands of the maker,
and with careful use will never be deranged.
245. The Adjustment of the Index Mirror consists in making the reflecting
surface of this mirror truly perpendicular to the plane of the sextant. In order to
test this, set the index near the middle of the arc, then, placing the eye very nearly
in the plane of the sextant and close to the index mirror, observe whether the direct
image of the arc and its image reflected from the mirror appear to form one continuous
arc ; if so, the glass is perpendicular to the plane of the sextant ; if the reflected image
appears to droop from the arc seen directly, the glass leans backward; if it seems to
rise, the glass leans forward. The adjustment is made by the screws at the back of
the mirror.
246. The Adjustment of the Horizon Mirror consists hi making the reflecting
surface of this mirror perpendicular to the plane of the sextant. The index mirror
having been adjusted, if, in revolving it by means of the index arm, there is found
one position in which it is par ah 1 el to the horizon glass, then the latter must also be
perpendicular to the plane of the sextant. In order to test this, put in the telescope
and direct it toward a star; move the index until the reflected image appears to pass
the direct image; if one passes directly over the other the mirrors must be parallel;
94 INSTRUMENTS EMPLOYED IN NAUTICAL ASTRONOMY.
if one passes on either side of the other the horizon glass needs adjustment, which is
accomplished by means of the screws attached.
The sea horizon may also be used for making this adjustment. Hold the sextant
vertically and bring the direct and the reflected images of the horizon line into coin
cidence; then incline the sextant until its plane makes but a small angle with the
horizon; if the images still coincide the glasses are parallel; if not, the horizon glass
needs adjustment.
247. The Adjustment of the Telescope must be so made that, in measuring
angular distances, the line of sight, or axis of the telescope, shall be parallel to the
plane of the instrument, as a deviation in that respect, in measuring large angles,
will occasion a considerable error. To avoid such error, a telescope is employed in
which are placed two wires, parallel to each other and equidistant from the center
of the telescope; by means of these wires the adjustment may be made. Screw on
the telescope, and turn the tube containing the eyeglass till the wires are parallel
to the plane of the instrument; then select two clearly defined objects whose angular
distance must be not less than 90, because an error is more easily discovered when
the angle is great; bring the reflected image of one object into exact coincidence
with the direct image of the other at the inner wire; then, by altering slightly the
position of the instrument, make the objects appear on the other wire; if the contact
still remains perfect, the axis of the telescope is in its right situation; but if the two
objects appear to separate or lap over at the outer wire the telescope is not parallel,
and it must be rectified by turning one of the two screws of the ring into which the
telescope is screwed, having previously unturned the other screw; by repeating this
operation a few times the contact will be precisely the same at both wires, and the
axis of the telescope will be parallel to the plane of the instrument.
Another method of making this adjustment is to place the sextant upon a table
in a horizontal position, look along the plane of the limb, and make a mark upon a
wall, or other vertical surface, at a distance of about 20 feet; draw another mark
above the first at a distance equal to the height of the axis of the telescope above
the plane of the limb; then so adjust the telescope that the upper mark, as viewed
through the telescope, falls midway between the wires. Some sextants are accom
panied by small sights whose height is exactly equal to the distance between the
telescope and the plane of the limb ; by the use of these, the necessity for employing
the second mark is avoided and the adjustment can be very accurately made.
248. The errors which arise from defects in what have been denominated the
permanent adjustments of the sextant may be divided into three classes, namely:
Errors due to faulty centering of the axis, called eccentricity; errors of graduation;
and errors arising from lack of parallelism of surfaces in index mirror and in shade
glasses.
The errors due to eccentricity and faulty graduation are constant for the same
angle, and should be determined once for all at some place where proper facilities
for doing the work are at hand; these errors can only be ascertained by measuring
known angles with the sextant. If angles of 10, 20, 30, 40, etc., are first laid
off with a theodolite or similar instrument and then measured by the sextant, a
table of errors of the sextant due to eccentricity and faulty graduation may be made,
and the error at any intermediate angle found by interpolation; this table will
include the error of graduation of the theodolite and also the error due to inaccurate
reading of the sextant, but such errors are small. Another method for determining
the combined errors of eccentricity and graduation is by measuring the angular
distance between stars and comparing the observed and the computed arc between
them, but this process is liable to inaccuracies by reason of the uncertainty of allow
ances for atmospheric refraction.
Errors of graduation, when large, may be detected by "stepping off" distances
on the graduated arc with the vernier ; place the zero of the vernier in exact coinci
dence with a division of the arc, and observe whether the filial division of the vernier
also coincides with a division of the arc; this should be tried at numerous positions
of the graduated limb, and the agreement ought to be perfect in every case.
The error due to a prismatic index mirror may be found by measuring a certain
unchangeable angle, then taking out the glass and turning the upper edge down,
and measuring the angle again; half the difference of these two measures will be
the error at that angle due to the mirror. From a number of measures of angles
INSTRUMENTS EMPLOYED IN NAUTICAL ASTRONOMY. 95
in this manner, a table similar to the one for eccentricity and faulty graduation can
be made ; or the two tables may be combined. When possible to avoid it, however,
no sextant should be used in which there is an index mirror which produces a greater
error than that due to the probable error of reading the scale. Mirrors having a
greater angle than 2" between their faces are rejected for use in the United States
Navy. Index mirrors may be roughly tested by noting if there is an elongated
image of a well-defined point at large angles.
Since the error due to a prismatic horizon mirror is included in the index cor
rection (art. 249), and consequently applied alike to all angles, it may be neglected.
Errors due to prismatic shade glasses can be determined by measuring angles
with and without the shade glasses and noting the difference. They may also be
determined, where the glasses are so arranged that they can be turned through an
angle of 180, by measuring the angle first with the glass in its usual position and
then reversed, and taking the mean of the two as the true measure.
249. INDEX ERROR. The Index Error of a sextant is the error of its indications
due to the fact that when the index and horizon mirrors are parallel the zero of the
vernier does not coincide with the zero of the scale. Having made the adjustments
of the index and horizon mirrors and of the telescope, as previously described, it is
necessary to find that point of the arc at which the zero of the vernier falls when the
two mirrors are parallel, for all angles measured by the sextant are reckoned from
that point. If this point is to the left of the zero of the limb, all readings will be
too great; if to the right of the zero, all readings will be too small.
If desirable that the reading should be zero when the mirrors are parallel, place
the zero of the vernier on zero of the arc; then, by means of the adjusting screws of
the horizon glass, move that glass until the direct and reflected images of the same
object coincide, after which the perpendicularity of the horizon glass should again be
verified, as it may have been deranged by the operation. This adjustment is not
essential, since the correction may readily be determined and applied to the reading.
In certain sextant work, however, such as surveying, it will be very convenient to
be relieved of the necessity of correcting each angle observed. The sextant should
never be relied upon for maintaining a constant index correction, and the error
should be ascertained frequently. It is a good practice to verify the correction each
time a sight is taken.
250. The Index Correction may be found (a) by a star, (6) by the sea horizon,
and (c) by the sun.
(a) Bring the direct and reflected images of a star into coincidence, and read off
the arc. The index correction is numerically equal to this reading, and is positive
or negative according as the reading is on the right or left of the zero.
(6) The same method may be employed, substituting for a star the sea horizon,
though this will be found somewhat less accurate.
(c) Measure the apparent diameter of the sun by first bringing the upper limb
of the reflected image to touch the lower limb of the direct image, and then Winging
the lower limb of the reflected image to touch the upper limb of the direct image.
Denote the readings in the two cases by r and r r ; then, if S = apparent diameter
of the sun, and II = the reading of the sextant when the two images are in coincidence,
we have:
r =
r =R-S,
As R represents the error, the correction will be R. Hence the rule: Mark the
readings when on the arc with the negative sign; when off, with the positive sign;
then the index correction is one-half the algebraic sum of the two readings.
EXAMPLE : The sun s diameter is measured for index correction as follows : On
the arc, 31 20"; off the arc, 33 10". Required the correction.
On the arc, -31 20"
Off the arc, +33 10
2^+1 50
T C... + RR
96 INSTRUMENTS EMPLOYED IN NAUTICAL ASTRONOMY.
251. From the equations previously given, it is seen that:
S-* (r-rO;
hence, if the observations are correct, it will be found that the sun s semidiameter,
as given in the Nautical Almanac for the day of observation, is equal to one-half the
algebraic difference of the readings. If required to obtain the index correction with
great precision, several observations should be taken and the mean used, the accuracy
being verified by comparing the tabulated with the observed semidiameter. If the
sun is low, the horizontal semidiameter should be observed, to prevent the error that
may arise from unequal refraction.
252. USE OP THE SEXTANT. To measure the angle between any two visible
objects, point the telescope toward the lower one, if one is above the other, or toward
the left-hand one, if they are in nearly the same horizontal plane. Keep this object
in direct view through the unsilvered part of the horizon glass, and move the index
arm until the image of the other object is seen by a double reflection from the index
mirror and the silvered portion of the horizon glass. Having gotten the direct
image of one object into nearly exact contact with the reflected image of the other,
clamp the index arm and, by means of the tangent screw, complete the adjustment
so that the contact may be perfect; then read the limb.
In measuring the altitude of a celestial body above the sea horizon, it is necessary
that the angle shall be measured to that point of the horizon which lies vertically
beneath the object. To determine this point, the observer should move the instru
ment slightly to the right and left of the vertical, swinging it about the line of sight
as^an axis, taking care to keep the object in the middle of the field of view. The
object will appear to describe the arc of a circle, and the lowest point of this arc
marks the true vertical.
The shade glasses should be employed as may be necessary to protect the eye
when observing objects of dazzling brightness, such as the sun, or the horizon when
the sun is reflected from it at a low altitude. Care must be taken that the images
are not too bright or the eye will be so affected as to interfere with the accuracy of
the observations.
253. CHOICE OF SEXTANTS. The choice of a sextant should be governed by the
kind of work which is required to be done. In rough work, such as surveying, where
angles need only be measured to the nearest 30" the radius maybe as small as 6 inches,
which will permit easy reading, and the instrument can be correspondingly lightened.
Where readings to 10" are desired, as in nice astronomical work, the radius should be
about 7J inches, and the instrument, to be strongly built, should weigh about 3J
pounds.
The parts of an instrument should move freely, without binding or gritting. The
eyepieces should move easily in the telescope tubes ; the bracket for carrying the tele
scope should be made very strong. It is frequently found that the parallelism of
the line of sight is destroyed in focusing the eyepiece, either on account of the loose
ness of the fit or because of the telescope bracket being weak. The vernier should
lie close to the limbs to prevent parallax in reading. If it is either too loose or too
tight at either extremity of its travel, it may indicate that the pivot is not perpendicu
lar. The balls of the tangent screw should fit snugly in their sockets, so that there
may be no lost motion.
Where possible, the sextant should always be submitted to expert examination
and test as to the accuracy of its permanent adjustments before acceptance by the
navigator.
254. RESILVERING MIRRORS. Occasion may sometimes arise for resilvering the
mirrors of a sextant, as they are always liable to be damaged by dampness or other
causes. For this purpose some clean tin foil and mercury are required. Upon a
piece of glass about 4 inches square lay a piece of tin foil whose dimensions exceed by
about a quarter of an inch in each direction those of the glass to be silvered; smooth
put the foil carefully by rubbing; put a small drop of mercury on the foil and spread
it with the finger over the entire surface, being careful that none shall find its waj
under the foil; then put on a few more drops of mercury until the whole surface is
fluid. The glass which is to be silvered having been carefully cleaned, it should be
laid upon a piece of tissue paper whose edge just covers the edge of the foil and
INSTRUMENTS EMPLOYED IN NAUTICAL ASTRONOMY. 97
transferred carefully from the paper to the tin foil, a gentle pressure being kept upon
the glass to avoid the formation of bubbles; finally, place the mirror face downward
and leave it in an inclined position to allow the surplus mercury to flow off, the latter
operation being hastened by a strip of tin foil at its lower edge. After five or six
hours the tin foil around the edges may be removed, and the next day a coat of
varnish made from spirits of wine and red sealing wax should be applied. For a
horizon mirror care must be taken to avoid silvering the plain half. The mercury
drawn from the foil should not be placed with clean mercury with a view to use in the
artificial horizon or the whole will be spoiled.
255. OCTANTS AND QUIXTANTS. Properly speaking, a sextant is an instrument
whose arc covers one-sixth of a complete circle, and which is therefore capable of
measuring an angle of 120. Other instruments are made which are identical in
principle with the sextant as heretofore described, and which differ from that instru
ment only in the length of the arc. These are the octant, an eighth of a circle, by
which angles may be measured to 90, and the quintant, a fifth of a circle, whicn
measures angles up to 144. The distinction between these instruments is not
always carefully made, and in such matters as have been touched upon in the fore
going articles the sextant may be regarded as the type of all kindred reflecting
instruments.
THE ARTIFICIAL HORIZON.
256. The Artificial Horizon is a small, rectangular, shallow basin of mercury,
over which, to protect the mercury from agitation by the wind, is placed a roof
consisting of two plates of glass at right angles to each other. The mercury affords
a perfectly horizontal surface which is at the same time an excellent mirror. The
different parts of an artificial horizon are furnished in
a compact form, a metal bottle being provided for
containing the mercury when not in use, together
with a suitable funnel for pouring.
If MN, in figure 34, is the horizontal surface of
the mercury; S B a ray of light from a celestial
object, incident to the surface at B ; BA the reflected
ray; then an observer at A will receive the ray BA
as if it proceeded from a point S", whose angular
depression, MBS", below the horizontal plane is
equal to the altitude, MBS , of the object above
that plane. If, then, SA is a direct ray from the
object parallel to S B, an observer at A can measure
with the sextant the angle SAS" = S BS" = 2 S BM, by
bringing the image of the object reflected by the
index mirror into coincidence with the image S* re
flected by the mercury and seen through the horizon
glass. The instrumental measure, corrected for in
dex error, will be double the apparent altitude of the F IG . 34 .
body.
The sun s altitude will be measured by bringing the lower limb of one image to
touch the upper limb of the other. Half the corrected instrumental reading wiU be
the apparent altitude of the sun s lower or upper limb, according as the lower or upper
limb of the reflected image was the one employed in the observation.
In observations of the sun with the artificial horizon, the eye is protected by a
single dark glass over the eyepiece of the telescope through which direct and reflected
rays must pass alike, thereby avoiding the errors that might possibly arise from a
difference in the separate shade glasses attached to the frame of the sextant.
The glasses in the roof over the mercury should be made of plate glass, with
perfectly parallel faces. If they are at all prismatic, the observed altitude will be
erroneous. The error may be removed by observing a second altitude with the roof
reversed, and, in general, by taking one-half of a set of observations with the roof in
one position and the other half with the roof reversed. On the rare occasions when
the atmosphere is so calm that the unsheltered mercury will remain undisturbed,
most satisfactory observations may be made by leaving off the roof.
61828
98 INSTRUMENTS EMPLOYED IN NAUTICAL ASTRONOMY.
257. In setting up an artificial horizon, care should be taken that the basin is
free from dust and other foreign matter, as small particles floating upon the surface
of the mercury interfere with a perfect reflection. The basin should be so placed
that its longer edge lies in the direction in which the observed body will bear at the
middle of the observations. The spot selected for taking the sights should be as
free as possible from causes which will produce vibration of the mercury, and pre
cautions should be taken to shelter the horizon from the wind, as the mere placing
of the roof will not ordinarily be sufficient to accomplish this. Embedding the roof
in earth serves to keep out the wind, while setting the whole horizon upon a thick
towel or a piece of such material as heavy felt usually affords ample protection from
wind, tends to reduce the vibrations from mechanical shocks, and also aids in keeping
out the moisture from the ground. In damp climates the roof should be kept dry
by wiping, or the moisture deposited from the inclosed air will form a cloud upon
the glass.
Molasses, oil, or other viscous fluid may, when necessary, be employed as a
substitute for mercury.
258. Owing to the perfection of manufacture that is required to insure accuracy
of results with the artificial horizon, navigators are advised to accept only such
instrument as has satisfactorily stood the necessary tests to prove the correctness of
its adjustment as regards the glasses of the roof.
THE CHRONOMETER.
259. The Chronometer is simply ^ a correct time measurer, differing from an
ordinary watch in having the force of its mainspring rendered uniform by means of
a variable lever. Owing to the fact^that on a sea voyage a chronometer is exposed
to many changes of temperature, it is furnished with an expansion balance, formed
of a combination of metals of different expansive qualities, which produces the
required compensation. In order that its working may not be deranged by the
motion of the ship in a seaway, the instrument is carried in gimbals.
As the regularity of the chronometer is essential for the correct determination
of a ship s position, it is of the greatest importance that every precaution be taken
to insure the accuracy of its indications. There is no more certain way of doing
this than to provide a vessel with several of these instruments preferably not less
than three in order that if an irregularity develop in one, the fact may be revealed
by the others.
260. CARE OF CHRONOMETERS ON SHIPBOARD. The box in which the chro
nometers are kept should have a permanent place as near as practicable to the center
of motion of the ship, and where it will be free from excessive shocks and jars, such
as those that arise from the engines or from the firing of heavy guns; the location
should be one free from sudden and extreme changes of temperature, and as far
removed as possible from masses of vertical iron. The box should contain a separate
compartment for each chronometer, and each compartment should be lined with
baize cloth padded with curled hair, for the double purpose of reducing shocks and
equalizing the temperature within. An outer cover of baize cloth should be pro
vided for the box, and this should be changed or dried out frequently in damp
weather. The chronometers should all be placed with the XII mark in the same
position.
For transportation for short distances by hand, an instrument should be rigidly
clamped in its gimbals, for if left free to swing, its performance may be deranged by
the violent oscillations that are imparted to it.
For transportation for a considerable distance, as by express, the chronometer
should be allowed to run down, and should then be dismounted and the balance
corked.
261. Since it is not possible to make a perfect instrument which will be unin
fluenced by the disturbing causes incident to a sea voyage, it becomes the duty of
the navigator to determine the error and to keep watch upon the variable rate of the
chronometer.
The error of the chronometer is the difference between the time indicated and the
standard time to which it is referred usually Greenwich mean time.
The amount the chronometer gains or loses daily is the daily rate.
INSTRUMENTS EMPLOYED IN NAUTICAL ASTRONOMY.
99
The indications of a chronometer at any given instant require a correction for
the accumulated error to that instant; and this can be found if the error at any
given time, together with the daily rate, are known.
262. WINDING. Chronometers are ordinarily constructed to run for 56 hours
without rewinding, and an indicator on the face always shows how many hours
have elapsed since the last winding. To insure a uniform rate, they must be wound
regularly every day, and, in order to avoid the serious consequences of their running
down, the navigator should take some means to guard against neglecting this duty
through a fault of memory. To wind, turn the chronometer gently on its side,
enter the key in its hole and push it home, steadying the instrument with the hand,
and wind to^the left, the last half turn being made so as to bring up gently against
the stop. After winding, cover the keyhole and return the instrument to its natural
position. Chronometers should always be wound in the same order to prevent
omissions, and the precaution taken to inspect the indicators, as a further assurance
of the proper performance of the operation.
After winding each day, the comparisons should be made, and, with the readings
of the maximum-and-minimum thermometer and other necessary data, recorded in
a book kept for the purpose.
The maximum-and-mininium thermometer is one so arranged that its highest
and lowest readings are marked by small steel indices that remain in place until
reset. Every chronometer box should be provided with such an instrument, as a
knowledge of the temperature to which chronometers have been subjected is essential
in any analysis of the rate. To draw down the indices for the purpose of resetting,
a magnet is used. This magnet should be kept at all times at a distance from the
chronometers.
263. COMPARISON OF CHRONOMETERS. The instrument ^believed to be the best
is regarded as the Standard, and each other is compared with it. It is usual to desig
nate the Standard as A, and the others as B, C, etc. Chronometers are made to
beat half seconds, and any two may be compared by following the beat of one with
the ear and of the other with the eye.
To make a comparison, say of A and B, open the boxes of these two instruments
and close all others. Get the cadence and, commencing when A has just completed
the beat of some even 5-second division of the dial, count " h^lf -one-half- two-half-
three-half -four-half -five/ glancing at B in time to note the position of its second hand
at the last count; the seconds indicated by A will be five greater than the number
at the beginning of the count. The hours and minutes are also recorded for each
chronometer, and the subtraction made. A good check upon the accuracy is afforded
by repeating the operation, taking the tick from B.
Where necessary for exact work, it is possible to estimate the fraction between
beats, and thus make the comparison to tenths of a second; but the nearest half
second is sufficiently exact for the purposes of ordinary navigation at sea.
264. The following form represents a convenient method of recording com
parisons :
STAND. A, No. 777.
CHRO. B, No. 1509.
CHRO. C, No. 1802.
Designation of
Chro. B
with
9f\ riiff
Chro. C
with
2d rliff
rherm
L
T> ftr
PomarVe
comparisons.
Stand. A.
Stand. A.
Max.
Min.
Air.
January
1
Stand. A.
BandC.
h. m. s.
1 13 40
1 12,21.5
s.
h. m. s,
1 14 20
2 04 11
8.
|
63
59
60
30.07
Found errors
by time-
hall
Difference.
1 18.5
-
11 10 09
-
2
Stand. A.
BandC.
1 16 30
1 15 10
1 17 00
2 06 51. 5
64
58
57
30.12
Left New
York for
Difference.
1 20
+ 1.5
11 10 08. 5
-0.5
P. R.
100 INSTRUMENTS EMPLOYED IN NAUTICAL ASTRONOMY.
265. The second difference in the form is the difference between the comparisons
of the same instruments for two successive days. When a vessel is equipped with
only one chronometer there is nothing to indicate any irregularity that it may develop
at sea and even the best instruments may undergo changes from no apparent cause.
When there are two chronometers, the second difference, which is equal to the algebraic
difference between their daily rates, remains uniform as long as the rates remain
uniform, but changes if one of the rates undergoes a change; in such a case, there is
no mefcns of knowing which chronometer has departed from its expected performance,
and the navigator must proceed with caution, giving due faith to the indications of
each. If, however, there are three chronometers, an irregularity on the part of one
is at once located by a comparison of the second differences. Thus, if the predicted
rates of the chronometers were such as to give for the second difference of A B, +
1 s . 5, and of A C, s . 5, suppose on a certain day those differences were + 4 s . 5 and s . 5,
respectively; it would at once be suspected that the irregularity was in B, and that
that chronometer had lost 3 s on its normal rate during the preceding day. Suppose,
however, the second differences were + 4 8 .5 and -f 2 S .5; it would then be apparent
that A had gained 3 s .
266. TEMPERATURE CURVES. Notwithstanding the care taken to eliminate the
effect of a change of temperature upon the rate of a chronometer, it is rare that an
absolutely perfect compensation is attained, and it may therefore be assumed that the
rates of all chronometers vary somewhat with the temperature. Where the voyage
of a vessel is a long one and marked changes of climate are encountered, the accu
mulated error from the use of an incorrect rate may be very material, amounting to
several minutes difference of longitude. Careful navigators will therefore take every
means to guard against such an error. By the employment of a temperature curve in
connection with the chronometer rate the most satisfactory results are arrived at.
267. There should be furnished with each chronometer a statement showing
its daily rate under various conditions of temperature; and this may be supplemented
by the observations of the navigator during the tune that the chronometer remains
on board ship. With all available data a temperature curve should be constructed
which will indicate graphically the performance of the instrument. It is most con
venient to employ for this purpose a piece of " profile paper," on which parallel lines
are ruled at equal intervals at right angles to each other. Let each horizontal line
represent, say, a degree of temperature, numbered at the left edge, from the bottom
up ; draw a vertical line in red ink to represent the zero rate, ana let all rates to the
right be plus, or gaining, and those to the left minus, or losing; let the intervals
between vertical lines represent intervals of rate (as one- tenth of a second) numbered
at the top from the zero rate; then on this scale plot the rate corresponding to each
temperature; when there are several observations covering one height of the ther
mometer, the mean may be used. Through all the plotted points draw a fair curve,
and the intersection of this curve with each temperature line gives the mean rate
at that temperature. The mean temperature given by the maximum and minimum
thermometer shows the rate to be used on any day.
268. HACK OR COMPARING WATCH. In order to avoid derangement, the chro
nometers should never be removed from the permanent box in which they are kept
on shipboard. Wh en it is desired to mark a certain instant of time, as for an astro
nomical observation or for obtaining the chronometer error by signal, the time is
marked by a "hack" (an inferior chronometer used for this purpose only), or by a
comparing watch. Careful comparisons are taken preferably both before and
afterwards and the chronometer time at the required instant is thus deduced. The
correction represented by the chronometer time minus the watch time (twelve hours
being added to the former when necessary to make the subtraction possible) is referred
to asC-W.
Suppose, for example, the chronometer and watch are compared and their
indications are as follows :
Chro. t., 5 h 27 m 30"
W. T., -2 36 45.5
C-W, 2 50 44.5
INSTRUMENTS EMPLOYED IN NAUTICAL ASTRO>CMY.
101
If then a sight is taken when the watch shows 3 h Ol ra , 27* 5, we
W. T., 3 h Ol m 27 8 .5
C-W, +2 50 44.5
Chro. t., 5 52 12.0
It may occur that the values of C W, as obtained from comparisons before and
after marking the desired time, will vary; in that case the value to be used will be
the mean of the two, if the tune marked is about midway between comparisons, but
if much nearer to one comparison than the other, allowance should be made accord
ingly-
Thus suppose, in the case previously given, a second comparison had been taken
after the sight as follows:
Chro. t., 6 h 12 m 45 s
W. T., -3 21 59.5
C-W,
2 50 45. 5
The sight having been taken at about the middle of the interval, the C W to
be used would be the mean of the two, or 2 h 50 m 45 s .O.
Let us assume, however, that the second comparison showed the following:
Chro. t., 6 h 38 m 25 8
W. T., -3 47 39
C-W,
2 50 46
Then, the sight having been taken when only about one-third of the interval
had elapsed between the first and second comparisons, it would be assumed that
only one-third of the total change in the C W had occurred up to the time of sight,
and the value to be used would be 2 h 50 m 45 s .O.
269. It is considered a good practice always to subtract watch time from
chronometer tune, whatever the relative values, and thus to employ C W invariably
as an additive correction. It is equally correct to take the other difference, W C,
and make it sub tractive ; it may sometimes occur that a few figures will thus be saved,
but a chance for error arises from the possibility of inadvertently using the wrong
sign, which is almost impossible by the other method. Thus, the following example
may be taken:
C, 10 h 57 m 38 s W,
Comparison^ ~ U 42 35 C >
-10
42 m 35 s
57 38
lC-W, 11 15 03 W-C, 44 57
Sight
11 50 21
|C-W, +11 15 03
W, 11 50 21
W-C, - 44 57
11 05 24
C,
11 05 24
CHAPTER IX.
TIME AND THE NAUTICAL ALMANAC.
270. The subjects of Time and the Nautical Almanac are two of the most
important ones to be mastered in the^ study of Nautical Astronomy, as they enter
into every operation for the astronomical determination of a ship s position. They
will be treated in conjunction, as the two are interdependent.
METHODS OF BECKONING TIME.
271. The instant at which any point of the celestial sphere is on the meriolian
of an observer is termed the transit, culmination, or meridian passage of that point;
when on that half of the meridian which contains the zenith, it is designated as
superior or upper transit; when on the half containing the nadir, as inferior or lower
transit.
272. Three different kinds of time are employed in astronomy (a) apparent
or solar time, (&) mean time, and (c) sidereal time. These depend upon the hour
angle from the meridian of the points to which they respectively refer. The point
of reference for apparent or solar time is the Center of the Sun; for mean tune, an
imaginary point called the Mean Sun; and for sidereal time, the Vernal Eguinox,
also called the First Point of Aries.
The unit of time is the Day, which is the period between two successive transits
over the same branch of the meridian of the point of reference. The day is divided
into 24 equal parts, called Hours; each hour is divided into 60 equal parts, called
Minutes, and each minute into 60 equal parts, called Seconds.
273. APPARENT OR SOLAR TIME. The hour angle of the center of the sun affords
a measure of Apparent or Solar Time. An Apparent or Solar Day is the interval of
tune between two successive transits over the same meridian 01 the center of the
sun. It is Apparent Noon when the sun s hour circle coincides with the celestial
meridian. This is the most natural and direct measure of time, and the unit of
time adopted by the navigator at sea is the apparent solar day. Apparent noon is
the time when the latitude can be most readily determined, and the ordinary method
of determining the longitude by the sun involves a calculation to deduce the apparent
time first.
Since, however, the intervals between the successive returns of the sun to the
same meridian are not equal, apparent time can not be taken as a standard. The
apparent day varies in length from two causes: first, the sun does not move in the
equator, the great circle perpendicular to the axis of rotation of the earth, but in the
ecliptic; and, secondly, the sun s motion in the ecliptic is not uniform. Sometimes
the sun describes an arc of 57 of the ecliptic, and sometimes an arc of 61 in a day.
At the points where the ecliptic and equinoctial intersect, the direction of the sun s
apparent motion is inclined at an angle of 23 27 to the equator, while at the solstices
it moves in a direction parallel to the equator.
274. MEAN TIME. To avoid the irregularity of time caused bv the want of
uniformity in the sun s motion, a fictitious sun, called the Mean Sun, is supposed to
move in the equinoctial with a uniform velocity that equals the mean velocity of the
true sun in the ecliptic. This mean sun is regarded as being in coincidence with the
true sun at the vernal equinox, or First Point of Aries.
Mean Time is the hour angle of the mean sun. A Mean Day is the interval
between two successive transits of the mean sun over the meridian. Mean Noon is
the instant when the mean sun s hour circle coincides with the meridian.
102
TIME AND THE NAUTICAL ALMANAC. 103
Mean time lapses uniformly; at certain times it agrees with apparent time,
while sometimes it is behind, ana at other times in advance of it. It is tnis time that
is measured by the clocks in ordinary use, and to tnis the chronometers used by
navigators are regulated.
275. The difference between apparent and mean tune is called the Equation of
Time; by this quantity, the conversion from one to the other of these tunes may be
made. Its magnitude and the direction of its application may be found for any
moment from the Nautical Almanac.
276. SIDEREAL TIME. Sidereal Time is the hour angle of the First Point of
Aries. This point, which is identical with the vernal equinox, is the origin of all
coordinates of right ascension. Since the position of the point is fixed hi the celestial
sphere and does not, like the sun, moon, and planets, have actual or apparent motion
tnerein, it shares in this respect the properties of the fixed stars. It may therefore
be said that intervals of sidereal tune are those which are measured by tne stars.
A Sidereal Day is the interval between two successive transits of me First Point
of Aries across the same meridian. Sidereal Noon is the instant at which the hour
circle of the First Point of Aries coincides with the meridian. In order to interconyert
sidereal and mean times an element is tabulated in the Nautical Almanac. This is
the Sidereal Time of Mean Noon, which is also the Right Ascension of the Mean Sun.
277. CIVIL AND ASTRONOMICAL TIME. The Civil Day commences at midnight
and comprises the twenty-four hours until the following midnight. The hours are
counted irom to 12, from midnight to noon; then, again, from to 12, from noon
to midnight. Thus the civil day is divided into two periods of twelve hours each,
the first of which is marked a. m. (ante meridian), while the last is marked p. m.
(post meridian).
The Astronomical or Solar Day commences at noon of the civil day of the same
date. It comprises twenty-four hours, reckoned from to 24, from noon of one day
to noon of the next. Astronomical time (apparent or mean) is the hour angle of the
sun (true or mean) measured to the westward throughout its entire circuit from the
time of its upper transit on one day to the same instant of the next.
The civfl day, therefore, begins twelve hours before the astronomical day, and
a clear understanding of this fact is all that is required for interconverting these
times. For example:
January 9, 2 a. m., civil time, is January 8, 14 h , astronomical tune.
January 9, 2 p. m., civil time, is January 9, 2 h , astronomical time.
278. HOUR ANGLE. The hour angle of a heavenly body is the angle at the
pole of the celestial concave between the declination circle of the heavenly body
and the celestial meridian. It is measured by the arc of the
celestial equator between the declination circle and the celestial
meridian.
In figure 35 let P be the pole of the celestial sphere, of which
VMQ is the equator, PQ the celestial meridian, and PM, PS,
PV the declination circles of the mean sun, a heavenly body,
and the First Point of Aries, respectively.
Then QPM, or its arc QM, is the hour angle of the mean
sun, or the mean time; QPS, or QS, the hour angle of the
heavenly body; QPV, or QV, the hour angle of the First Point
of Aries, or the sidereal time; VPQ, or VQ, the right ascension of the meridian; VPS,
or VS, the right ascension of the heavenly body; and VPM, or YM, the right ascen
sion of the mean sun.
279. TIME AT DIFFERENT MERIDIANS. The hour angle of the true sun at any
meridian is called the local apparent time; that of the mean sun, the local mean time;
that of the First Point of Aries, the local sidereal time. The hour angles of the same
body and points from Greenwich are respectively the Greenwich apparent, mean,
and sidereal times^. The difference between the local time at any meridian and the
Greenwich time is equal to the longitude of that place from Greenwich expressed
in time; the conversion from time to arc may be effected by a simple mathematical
calculation or by the use of Table 7.
In comparing corresponding times of different meridians the most easterly
meridian may be distinguished as that at which the time is greatest or latest.
104 TIME AND THE NAUTICAL ALMANAC.
In figure 36 PM and PM represent the celestial meridians of two places, PS
the declination circle through jhe sun, and PG the Greenwich meridian; let T Q = the
Greenwich tune = GPS ;
T M = the corresponding local time at all places on the meridian PM = MPS;
T M = the corresponding local time at all places on the meridian PM =M PS;
Lo = west longitude of meridian PM = GPM ; and
Lo = east longitude of meridian PM = GPM .
If west longitudes and hour angles be reckoned as positive,
and east longitudes and hour angles as negative, we have:
Lo = T G -T M ; and
Lo = T Q -T M ; therefore
LO-LO =T M -T M .
Thus it may be seen that the difference of longitude be
tween two places equals the difference of their local times.
FIG. 3c. This relation may be shown to hold for any two meridians
whatsoever.
Both local and Greenwich times in the above formulae must be reckoned west
ward, always from their respective meridians and from O h to 24 h ; in other words, it
is the astronomical tune which should be used in all astronomical computations.
The formula Lo = T G T M is true for any kind of time, solar or sidereal ; or, in general
terms, T G and T M are the hour angles of any point of the sphere at the two meridians
whose difference of longitude is Lo. S may be the sun (true or mean) or the vernal
equinox.
280. FINDING THE GREENWICH TIME. Since nearly every computation made
by the navigator requires a knowledge of the Greenwich date and time as a pre
liminary to the use of the Nautical Almanac, the first operation necessary is to
deduce from the local time the corresponding Greenwich date, either exact or approxi
mate, and thence the Greenwich time expressed astronomically.
The formula is:
remembering that west longitudes are positive, east longitudes are negative. Hence
the following rule for converting local to Greenwich time : .
Having expressed the local time astronomically, add the longitude if west,
subtract it u east; the result is the corresponding Greenwich time.
EXAMPLE: In longitude 81 15 W. the local time is, April, 15 d 10 h 17 m 30 s a. m. Required the
Greenwich time.
Local Ast. time, April, 14 d 22 h 17 m 30 s
Longitude, + 5 25 00
Greenwich time, 15 3 42 30
EXAMPLE: In longitude 81 15 E. the local time is, August, 5 d 2 h 10 m 30 p. m. Required the Green
wich time.
Local Ast. time, August, 5 d 2 h 10 m 30
Longitude, 5 25 00
Greenwich time, 4 20 45 30
EXAMPLE: In longitude 17 28 W. the local time is, May, l d 3 h 10 m p. m. Required the Greenwich
time.
Local Ast. time, May, l d 3 h 10 m 00 s
Longitude, + 1 09 52
Greenwich time, 1 4 19 52
EXAMPLE: In longitude 125 30 E. the local time is, May, l d 8 h 10 m 30 a. m. Required the Green
wich time.
Local Ast. time, April, 30 d 20 11 10 m 30 s
Longitude, - 8 22 00
Greenwich time, 30 11 48 30
TIME AND THE NAUTICAL ALMANAC. 105
281. From the preceding article we have:
T G =T M -fLo; hence,
T M =T G -Lo;
thus it will be seen that, to find the local time corresponding to any Greenwich time,
the above process is simply reversed.
Since all observations at sea are referred to chronometers regulated to Greenwich
mean time, and as these instruments are iisually marked on the dial from O h to 12 h , it
becomes necessary to distinguish whether it is a. m. or p. m. at Greenwich. Therefore
an approximate knowledge of the longitude and local time is necessary to determine
the Greenwich date.
EXAMPLE: In longitude 5 h 00 m 00* W., about 3 h 30 m p. m. April 15th, the Greenwich chronometer
read 8 h 25 m , and was fast of Gr. time 3 m 15 s . Required the local astronomical time.
Approx. local time, 15 d 3 h 30 m Gr. chro., 8 h 25 m 00 s Gr. Ast. time 15 d , 8 h 21 m 45
Longitude, + 5 00 Corr., 3 15 Longitude, 5 00 00
Approx. Gr. time, 15 8 30 Gr. Ast. time 15 d , 8 21 45 Local Ast. time 15 d , 3 21 45
EXAMPLE: In longitude 5 h 00 m 00 s E., about 8 a. m. May 3d, the Gr. chro. read 3 h 15 m 20 s , and was
fast of Gr. time 3 m 15 s . Required the local astronomical time.
Approx. local time, May, 2 d 20 h Gr. chro., 3 b 15 m 20* Gr. Ast. time2 d , 15 h 12 m 05 s
Longitude, 5 Corr., 3 15 Longitude, + 5 00 00
Approx. Gr. time, 2 15 Gr. Ast. time 2 d , 15 1205 Local Ast. time 2 d , 20 12 05
THE NAUTICAL ALMANACK
282. The American Ephermeris and Nautical Almanac is divided into three parts
as follows: Part I, Ephemeris for the meridian of Greenwich, gives the ephemerides
of the sun and moon, the geocentric and heliocentric positions of the major planets,
the sun s coordinates, and other fundamental astronomical data for equidistant
intervals of Greenwich mean time ; Part II, Ephemeris for the meridian of Washington
gives the ephemerides of the fixed stars, sun, moon, and major planets for transit
over the meridian of Washington, and Part III, Phenomena, contains predictions of
phenomena to be observed with data for their computation. Tables are also appended
for the interconversion of mean and sidereal time and for finding the latitude and
azimuth by an altitude of Polaris.
Tlie American Nautical Almanac is a smaller book made up of extracts from the
" Ephemeris and Almanac" just described, and is designed especially for the use of
navigators, being adapted to the meridian of Greenwich. It contains the position
of the sun and moon, together with the ephemerides of the planets Venus, Mars,
Jupiter, and Saturn, and the apparent places of 55 stars for the first of each month
and the Greenwich mean tune of transit at Greenwich for each of these stars, also the
mean places of 110 additional stars; solar and lunar eclipses are described, and the
tables for the interconversion of mean and sidereal time and for finding the latitude
by Polaris are included.
The elements dependent upon the sun and moon are placed in the first part of
the book, arranged according to hours, days, and months of the year. The right
ascension of the mean sun for the entire year is given at one opening, also, the mean
time of sidereal noon at Greenwich; the declination of the sun, equation of time, the
right ascension and decimation of the moon and the moon s horizontal parallax and
semidiameter are given for every even hour throughout the year. They must be
taken from the Almanac for some definite instant of Greenwich mean time. In
computations from observations that depend upon the time of the sun s meridian
passage, at which instant the local apparent time is O h , and the Greenwich apparent
time is equal to the longitude, if west, or to 24 h minus the longitude, if east, it
becomes necessary to correct the equation of time for longitude, before it is applied
a See extracts from Ephemeris and Nautical Almanac for 1916, Appendix I.
106 TIME AND THE NAUTICAL ALMANAC.
to the Greenwich apparent time to obtain a Greenwich mean time for use in
out other desired data. This Greenwich mean time is sufficiently correct for all
practical purposes as the equation of time never changes more than 1 8 .3 hi an hour.
283. KEDUCTION OF ELEMENTS. The reduction of elements in the Nautical
Almanac is usually accomplished by Interpolation, but in certain cases where extreme
precision is necessary the method of Second Differences must be used.
The Ephemeris, being computed for the Greenwich meridian, contains the right
ascensions, declinations, equations of time, and other elements for given equidistant
intervals of Greenwich time. Hence, before the value of any of these quantities can
be found for a given local time it is necessary to determine the corresponding Green
wich time. Should that time be one for which the Nautical Almanac gives the
value of the required element, nothing more is necessary than to employ that value.
But if the time falls between the Almanac times, the required quantity must be
found by interpolation.
The Almanac contains the rate of change or difference of each of the principal
quantities for some unit of time, and, unless great precision is required, the first
differences only need be regarded. In order to use the difference columns to advan
tage, the Greenwich date should be expressed in the unit of time for which the
difference is given. Thus, for using the hourly differences, the Greenwich time
should be expressed in hours and decimal parts of an hour; when using the differences
for one minute, the time should be in minutes and decimal parts of a minute. Instead
of using decimal parts, some may prefer the use of aliquot parts.
Since the quantities in the Almanac are approximate numbers, ^iven to a cer
tain decimal, any interpolation of a lower order than that decimal is unnecessary
work. Moreover, since, hi computations at sea, the Greenwich time is more or less
inexact, too great refinement need not be sought in reducing the Almanac elements.
Simple interpolation assumes that the differences of the quantities are
proportional to the differences of the times; in other words, that the differences
given in the Almanac are constant ; this is seldom the case, but the error arising from
the assumption will be smaller the less the interval between the times in the Almanac.
Hence those quantities which vary most irregularly are given for the smallest units
of time; as the variations are more regular, the units for which the differences are
given increase.
In taking from the Almanac the elements relating to the fixed stars the data
may be found either hi the table which gives the "mean place" of each star for the
year or in that which gives the " apparent place " occupied by each one on the first
day of each month. As the annual variation of position of the fixed stars is small,
the results will not vary greatly whichever table may be used. Yet, as it is proper
to seek always the greatest attainable accuracy, the use of the table showing the
exact positions is recommended.
284. To find from the Nautical Almanac a required element for any given time
and place, it is first necessary to express the time astronomically and to convert it
to Greenwich time and date. Then take from the Almanac, for the nearest given
preceding instant, the required quantity, together with its corresponding " hourly 5 or
" two-hourly difference," noting the name or sign in each case. Multiply the " hourly
difference" by the number of hours and fraction of an hour, or use Table IV, N. A.
(proportional parts), corresponding to the interval between the time for which the
quantity is given in the Almanac and the time for which required ; apply the correc
tion thus obtained, having regard to its sign.
A modification of this rule n
may be adopted if the time for which the quantity is
desired falls considerably nearer a subsequent time given in the Almanac than it does
to one preceding; in this case the interpolation may be made backward, the sign of
application of the correction being reversed.
TIME AND THE NAUTICAL ALMANAC.
107
EXAMPLE: At a place in longitude 81 15 W., April 17, 1916, find the sun s declination and the
equation of time at apparent noon.
G. A. T., 17 d ,
Eq. t.,
G. M. T., 17 d ,
Long. =81 15 W
5 h 25 m 00-
27
G. A. T.=17 d 5 h 25 m =17 d +5 h .42.
Eq. t.,17 d 4 h .
Corr.,
26M
+ .8
H. D.,+0-,6
Int., 1M2
5 2433 Eq. t., 17 d 5 h 25 m , 26.9
= 5 h .4 (Add to mean time.)
Dec., 17 d 4 h , 10 Sl .ON. H. D., +0 .9
Corr., + 1 .3 G. M. T., l h .4
Corr., +1^2
Corr., +0.852
Dec., 17 d 5 h 25 m , 10 32 .3 N.
EXAMPLE: At a place in longitude 81 15 E., April 17, 1916, find the sun s declination and the
equation of time at apparent noon.
Long. =81 15 E.
G. A. T.=16 d 18 h 35 m =17 d -5 h .42.
G.
Eq
G.
A.
. t,
M.
T.,
T.,
16 d ,
16 d ,
Dec.,
Corr.,
18 h 35 m
00 s
20
.5
Eq. t., 16 d 18 h , O m 20.2
Corr., + .3
H. D.,
Int.,
Corr.
MX.9
0^.58
s
O h
.6
.58
18 34
18 .58
16 d 18 h ,
39
.5
10
+
Eq. t., 16 d 18 h 35 m , 20.5
(Add to mean time.)
22 .2 N. H. D., -
.5 G. M. T.,
+0*
.348
Dec., 16 d 18 h 35 m , 10 22 .7 N. Corr., +(X.522
EXAMPLE: April 15, 1916, at ll h 55 m 30 s a. m., local mean time, in Long. 81 15 W., required the
declination and semidiameter of the sun, the equation of time, and the right ascension, declination,
horizontal parallax, and semidiameter of the moon and Jupiter.
Local mean time, 14 d 23 h 55 m 30 s
Longitude, + 5 25 00
f!5 5 20 30
Greenwich mean time, U5 d 5 h 20 m .5
[l5 d 5 h .34
For the Sun.
S. D., 15 58"
(Same as at G. A. Noon.)
Dec., 15 d 4 h ,
Corr., +
Dec.,
9 48 .5
1.2
9 49 .7
H. D., +
G. M. T.,
Corr., -f
.9
l h .34
1 .20
N.
Eq. t., 15 d 4 h ,
Corr.,
02 .8
0.8
02
R. A. 15 d 4 h ,
Corr.,
R. A.,
H. D.,
G. M. T.,
ll h 28 m 14 s
+ 2 38
11 30 52
+ 118 s
l h .34
For the Moon.
Hor.Par.,15 d 5 h .34, 57 .1
S. D., 15 d 5 h .34, 15 .6
Eq. t..
H. D.,
G. M. T.,
Corr., - 0-.804
(Subtract from fnean time.)
O s .6
l h .34
Corr.,
158 s
2 m 38 s
(By proportional parts Table IV, N. A.
R. A., 15 d 6 h , ll h 32 m 10 9
Corr.,39 m .5, - 1 18
Dec.,15 h 4 h ,
Corr.,
Dec..
H. D.,
G. M. T.,
Corr.,
39 7 .8S.
19 .8
59 .68.
14 X .7
l h .34
- 1978
(By proportional parts Table IV, N. A.)
R. A.,
11 30 52
R. A., 15 d O h .
Corr.,
R. A.,
H. D.,
G. M. T.,
, O h 56 m 28-
+ 12
56 40
-f 2 .25
5 h .34
For Jupiter.
Hor. Par., 15 d ,
S. D., 15 d ,
Dec.,15 d 6 h ,
Corr., 39 m .o.
Dec.,
+
09 X .3S.
19 .7
/ .02
(K.26
59 .68.
X.
Corr., + 12 s
(Prop, parts Table IV, N. A. (See p. 2536.))
R. A.,15 d O*, O h 56 m 28-
Corr., 5 h 20 m , + 12
R. A., 56 40
Dec., 15 d O h , + 4 5V. 5
Corr., + 1.2
Dec., 4 52 .7 X.
H. D., + / .23
G. M. T., 5 h .34
Corr., + 1^22
(Prop, parts Table IV, N. A.)
Dec., 15 d O b , + 4 5K5 N.
Corr., 5 h 20 m , + 1.2
Dec., 4 52 .7 N.
108 TIME AND THE NAUTICAL ALMANAC.
285. Should greater precision be required than that attainable by simple inter
polation, resort must be had to the reduction for second differences, for which use
the Ephemeris and Nautical Almanac.
The differences between successive values of the quantities given in the Ephem
eris and Nautical Almanac are called the first differences; the differences between
successive first differences are called the second differences. Simple interpolation,
which satisfies the necessities of sea computations, assumes the first differences to be
constant ; but if the variation of the first differences be regarded, a further interpo
lation is required for the second difference.
The difference for a unit of time in the American Ephemeris and Nautical
Almanac abreast any element expresses the rate at which the element is changing at
that precise instant of Greenwich time. Now, regarding the second difference as
constant, the first difference varies uniformly with the Greenwich time; therefore
its value may be found for any intermediate time by simple interpolation.
Hence the following rule for second differences : Employ the interpolated value
of the first difference which corresponds to the middle of the interval for which the
correction is to be computed.
EXAMPLE: For the Greenwich date 1916, April, 10 d 18 h 25 m 30 s , find the moon s declination.
Dec., 18 h , (+)21 09 41". 8 N. First diff., - 8".522 Second diff., -0".096
Corr., 3 37 .8 Corr., .020 Interval, +0 h .213
Dec., 21 06 04 N. M. D., - 8 .542 Corr., -0".020
No. min., + 25 m .5
Corr., -{
3 37".8
The difference for one minute being -8".522 at 18 h , and -8".618 at 19 h , the
difference for one minute undergoes a change of 0".096 during one hour. The
time for which it is desired to obtain the difference is at the middle instant between
18 h O m and 18 h 25 m .5 that is, at 18 h 12 m .75, or its equivalent, 18 h .213. With a
change of 0".096 in one hour, the change in O h .213 is readily obtainable; correcting
the minute s difference at 18 h .O accordingly, the process of correcting the declination
becomes the same as in simple interpolation.
CONVERSION OP TIMES.
286. Conversion of Time is the process by which any instant of time that is
defined according to one system of reckoning may be defined according to some other
system; and also by which any interval of time expressed in units of one system may
be converted into units of another.
287. SIDEREAL AND MEAN TIME. Mean time is the hour angle of the Mean
Sun; sidereal time is the hour angle of the First Point of Aries. Since the Right
Ascension of the Mean Sun is the angular distance between
the hour circles of the First Point of Aries and of the Mean
Sun, mean time may be converted into sidereal time by adding
to it the Right Ascension of the Mean Sun; and similarly,
p^ sidereal time may be converted into mean time by subtracting
from it the Right Ascension of the Mean Sun.
This is explained in figure 37, which represents a projec
tion of the celestial sphere upon the equator. If P be the
Pk?> QPQ ? the meridian; V, the First Point of Aries; M, the
position of the mean sun (west of the meridian) ; then QPV, or
Q the arc QV, is the sidereal time; QPM, or the arc QM, is the
FIG. 37. mean time; and VPM, or the arc VM, is the Right Ascension
of the Mean Sun. From this it will appear that :
or
Sidereal time = Mean time + Right Ascension of Mean Sun.
TIME AND THE NAUTICAL ALMANAC. 109
If the mean sun be on the opposite side of the meridian, at M , then the mean
time equals 24 h M Q. In this case:
= VM -M Q, or
Sidereal time = Right Ascension of Mean Sun (24 h Mean time),
= Right Ascension of Mean Sun -f Mean time 24 h .
Right ascension being measured to the east and hour angle to the wes% the
sidereal time will therefore always equal the sum of these two; but 24 h must be sub
tracted when the sum exceeds that amount.
From the preceding equations, we also have:
M = QV-VM; and
= VM -
M Q = VM -QV, or
(24 h -M Q) = (24 h + QV)-VM .
From this it may be seen that the mean time equals the sidereal time minus
the Right Ascension of the Mean Sun, but the former must be increased by 24 h
when necessary to make the subtraction possible.
288. APPARENT AND MEAN TIMES. Apparent tune is the angle between the
meridian and the hour circle which contains the center of the sun; mean time is the
angle between the meridian and the hour circle which contains the mean sun. Since
the equation of time represents the angle between the hour circles of the mean and
apparent suns, it is clear that the conversion of mean time to apparent time may be
accomplished by the application of the equation of time, with its proper sign, to
the mean time ; and the reverse operation by the application of the same quantity,
in an opposite direction, to the apparent time.
The resemblance of these operations to the interconversion of mean and sidereal
times may be observed if, in figure 37, we assume that PV is the hour circle of the
true sun, PM remaining that of the mean sun; then the arc QM will be the mean
time; QV, the apparent time; and VM, the equation of time; whence we have as
before :
QV = QM + VM, or
Apparent tune = Mean time + Equation of time;
the equation of time will be positive or negative according to the relative position of
the two suns.
289. SIDEREAL AND MEAN TIME INTERVALS. The sidereal year consists of
366.25636 sidereal days or of 365.25636 mean solar days. If, therefore, M be any
interval of mean time, and S the corresponding interval of sidereal time, the relations
between the two may be expressed as follows:
S_366. 25636
M ~365. 25636"
M 365. 25636 _
S ~ 366. 25636 - " 726
Therefore, 8=1.0027379 M = M + . 0027379 M;
M = 0.9972696 S =S -. 0027304 S.
If M = 24 h , S = 24 h + 3 m 56 S .6; or, in a mean solar day, sidereal time gains on
mean time 3 m 56 8 .6, the gain each hour being 9 S .S565.
If S = 24 h , M = 24 h 3 m 55 s . 9; or, in a sidereal day, mean tune loses on sidereal
time 3 m 55 8 .9, the loss each hour being 9 S .8296.
If M and S be expressed in hours and fractional parts thereof,
.8565M;
M= S-9 S .8296S.
Tables for the conversion of the intervals of mean into those of sidereal time
and the reverse are based upon these relations. Tables 8 and 9 of this work give
the values for making these conversions, and similar tables are to be found in the
Nautical Almanac.
110 TIME AND THE NAUTICAL ALMANAC.
290. To CONVERT MEAN SOLAR INTO SIDEREAL TIME. Apply to the local mean
time the longitude, adding if west and subtracting if east, and thus obtain the Green
wich mean time. Take from the Nautical Almanac the Right Ascension of the
Mean Sun at Greenwich mean noon, and correct it for the Greenwich mean time by
Table III, N. A., or Table 9 (Bowditch), or by the hourly difference of 9 S .857. Add
to the local mean time this corrected right ascension, rejecting 24 h if the sum is
greater than that amount. The result will be the local sidereal time.
EXAMPLE: April 22, 1916, in Long. 81 15 W., the local mean time is 2 b 00" 00* p. m. Required
the corresponding local sidereal time.
L. M. T., 22 d 2 h 00 m 00 R. A. M. S., 22 d O h , 2 h 00 m 50-.4 L. M. T., 2* 00 m 00-
Long., + 5 25 00 Red.for 7 h 25"(Tab. 9),-f I 13.1 R.A.M.S.,+ 2 02 03.5
G.M.T., 22 7 25 00 R. A. M. S., 7 h 25", 2 02 03.5 L. S. T., 4 02 03.5
EXAMPLE: April 22, 1916, in Long. 75 E., the local mean time is 4 h 00 00 a. m. Required the
local sidereal time.
L.M.T., 21 d 16 h 00 m 00- R. A. M. S., 21 d 0*, l h 56 53V8 L. M. T., 21 d 16 h 00" 00"
Long., 5 00 00 Red. for ll h (Tab. 9), -f 1 48 .4 R.A.M.S.,+ 1 58 42.2
G.M.T., 21 11 00 00 R.A.M.S., ll b , 1 58 42.2 L. S. T., 21 17 58 42.2
In these examples the reduction of the R-. A. M. S. has formed a separate opera
tion in order to make clear the process. It would be as accurate to add together
directly L. M. T., R. A. M. S., and Red., and the work would thus be rendered more
brief. r < i
291. To CONVERT SIDEREAL INTO MEAN SOLAR TIME. Take from the Nautical
Almanac the Right Ascension of the Mean Sun for Greenwich mean noon of the
given astronomical day, and apply to it the reduction for longitude, either by Table 9J
or by the hourly difference of 9 S .857, and the result will be the Right Ascension of;
the Mean Sun at local mean noon, which is equivalent to the local sidereal time at
that instant. Subtract this from the given local sidereal time (adding 24 h to the
latter if necessary), and the result will be the interval from local mean noon, expressed,
in units of sidereal time. Convert this sidereal time interval into a mean tune interval !
by subtracting the reduction as given by Table II, N. A., or Table 8, or by the hourlyj
difference of 9 8 .830; the result will be the local mean time.
EXAMPLE: April 22, 1916, a. m., in Long. 75 E., the local sidereal time is 17 h 58 m 42.2. _ What is;
the local mean time?
Astronomical day, April 21.
L. S. T., 17 h 58 m 42 8 .2 R. A. M. S., Gr. 21 d 0* l h 56 m 53.8
R. A. M. S., - 1 56 04 .5 Red. for -5 h long. (Tab. 9), r - 49 .3
Sid. interval from L. M. noon, 16 02 37.7 R. A. M. S., local O h , " 1 56 04.5
Red. for sid. interval (Tab. 8), 2 37 .7
L. M. T., 21 d , 16 00 00.0
EXAMPLE: April 22, 1916, p. m., at a place in Long. 81 15 W., the sidereal time is 4 h 02 m 03 8 .5.
What is the corresponding mean time?
Astronomical day, April 22.
L. S. T., 4 h 02 m 03-.5 R. A. M. S., Gr. 22 d 0", 2 h 00 m 50-.4
R. A. M. S., - 2 01 43.8 Red. for +5 h 25 m long. (Tab. 9),-f 53.4
Sid. interval from L. M. Noon, 2 00 19.7 R. A. M. S., local 0*, 2 01 43.8
Red. for sid. interval (Tab. 8),- 19 .7
L. M. T., 22 d , 2 00 00.0
292. To CONVERT MEAN INTO APPARENT TIME AND THE REVERSE. Find the
Greenwich time corresponding to the given local time. If apparent time is given,
find the Greenwich apparent time and take the equation of time from the Almanac.
If mean time, find the Greenwich mean time, correct the equation of time for the
required instant and apply it with its proper sign to the given time.
TIME AND THE NAUTICAL ALMANAC. Ill
EXAMPLE: April 21, 1916, in Long. 81 15 W., find the local apparent time corresponding to a local
mean time of 3 h 05 m 00" p. m.
L. M. T., 21 d 3 h 05 m 00* L. M. T., 21 d 3 h 05 m 00 Eq. t., 8 h , l m 21 8 .3
Long., + 5 25 00 Eq. t., + 1 21 .5 Corr., + 0.2
G. M. T., 21 8 30 00 L. A. T., 21 3 06 21 .5 Eq. t., 1 21. 5
H. D., + 0.5
G. M. T.,+ O h .5
Corr., + 8 .25
(Add to mean time.)
EXAMPLE: April 3, 1916, in Long. 81 15 E., the local apparent time is 8 h 45 m 00* a. m. Required
the mean time.
L A. T., 2 d 20 h 45 m CO- L. A. T., 2 d 20 11 45 m 00 Eq. t., 14 h , 3 m 30V6
Long., - 5 25 CO Eq. t., + 3 29 .7 Corr., - .9
G. A. T., 2 15 20 00 L. M. T., 2 20 48 29 .7 Eq. t., 3 29 .7
H. D., - 0-.7
Int., + l h .33
Corr., - O s .93
(Add to apparent time.)
293. To FIND THE HOUR ANGLE OF A BODY FROM THE TIME, AND THE
REVERSE. In figure 37, if M and M represent the positions of celestial bodies
instead of those of the mean sun as before assumed, then the hour angles of the
bodies will be Q M and 24 h M Q, respectively, and their right ascensions will be
T M and V M .
t As before, we have:
QV = QM + VM,
=VM -M Q;
QM =QV-VM;
M Q =VM -VQ, or
(24 h - M Q) = (24 h + Q V) - V M .
Substituting, therefore, hour angle of the body for mean time, and right ascension
of the body for Eight Ascension of the Mean Sun, the rules previously given for the
conversion of mean and sidereal times will be applicable for the conversion of hour
angle and sidereal time. Thus, the sidereal time is equal to the sum of the right
ascension of the body and its hour angle, subtracting 24 h when the sum exceeds
that amount ; and the hour angle equals the sidereal tune minus the right ascension
of the body, 24 h being added to the former when necessary to render the subtraction
possible.
EXAMPLE: In Long. 81 15 W., on April 25, 1916, at 12 h 10* 30- (astronomical) mean time, find the
hour angle of Sinus.
L. M. T., 12 h 10 m 30 L. M. T., 12 h 10* 30-.0
Long., + 5 25 00 R. A. M. S., 0*,+ 2 12 40 .0
Red. (Tab. 9), + 2 53 .4
G. M. T., 17 35 30
L. S. T., 14 26 03 .4
R. A. Sinus, - 6 41 27 .6
H. A. Sirius, 7 44 35 .8
EXAMPLE: May 9, 1916, Arcturus being 2 b 27 m 42V52 east of the meridian, find the local sidereal time.
24 h 00" 00- H. A., 21 h 32 m 17V48
H. A., 2 27 42.52 E. R. A., +14 11 52 .9
H. A., 21 32 17.48 W. L. S. T., 11 44 10 .38
Or thus:
H. A., - 2 h 27 m 42.52
R. A., +14 11 52 .9
L. S. T., 11 44 10 .38
112
TIME AND THE NAUTICAL ALMANAC.
294. M*ny navigators find the conversion of time much simplified and more
easily grasped by roughly plotting the elements as they are presented in any given
case, in a figure drawn on the plane of the celestial equator. Noting the known ele
ments and the elements required to be found, a study of the figure shows very
quickly how to combine the known elements to get the unknown elements.
Following this method, the examples of articles 290, 291, and 293 are here
solved as an alternative to the preceding treatment, since it is found that, for many
who have learned this method of procedure in the beginning, every difficulty in
reckoning or converting time has been obviated. Although the explanation may
appear somewhat long, the actual plotting and solution
of any given case take only a few seconds when the
method is understood. In the figures, P represents the
elevated pole; Q, the intersection of the local meridian
with the equator; G, the intersection of the meridian
of Greenwich with the equator; V, the First Point of
Aries (Vernal Equinox); S m , the mean sun; S a , the
apparent sun; and >K, a star or planet.
FIKST EXAMPLE OF ARTICLE 290. (SEE FIGURE 38.)
Draw a circle to represent the plane of the celestial
equator, P being the projection of the pole, and PQ the
projection of the local meridian. From P draw the
projection of the hour circle of the Greenwich meridian
which (since the longitude is west) is laid off to the right
or eastward of the local meridian so that the arc QG
Xals the longitude. The arrow indicates westerly direction and shows the direction in
ch the hour circles of the heavenly bodies move around the circle on the earth s axis.
The L. M. T. being p. m., we lay oft the hour circle of the mean sun to the westward
of the local meridian so that the arc QS m equals the L. M. T. We see at once from
the figure that the G. M. T. (the position of the hour circle of the mean sun, S m , with
reference to the Greenwich meridian) is the arc GQS m , which equals Long. + L. M. T.
Having thus found the G. M. T., we can find the right ascension of the mean sun at
that instant f rom the Nautical Almanac (picked out for the day and corrected for the
G. M. T.) which, in this case, is 2 h 02 m 03 S .5. The correction is ( + ) or additive to the
angle which represents the R. A. M. S. for Greenwich Mean Noon because this angle
has been increased by this amount owing to the
gain of the Vernal Equinox over the mean sun for
the angle through which the mean sun has traveled
from the Greenwich meridian. ^The mean sun is to
the eastward of the Vernal Equinox by the amount
of its right ascension. We therefore lay off PV,
the hour circle of the Vernal Equinox, so that the
arc VSm equals the R. A. M. S. Since the L. S. T.
equals the H. A. of the Vernal Equinox, we see at
once from the figure that the L. S. T. equals R. A. M.
S. + L.M.T.
SECOND EXAMPLE OF ARTICLE 290. (SEE FIGURE 39.)
FIG. 38.
FIG. 39.
Draw a circle to represent the plane of the celes
tial equator. Project the pole P and the local me
ridian JPQ. Draw the arrow pointed west to show the
direction in which the hour circles move. Since the longitude is east, we know that
the Greenwich meridian is to the westward of the local meridian, and we draw PG, the
Greenwich meridian, so that the arc QG equals the longitude, equals 5 hours. Since
the L. M. T. is 4 h 00 m 00 s a. m., we know that it will be 12 h -4 h equals 8 h before the
sun crosses the local meridian; hence we lay off the arc QS m to equal the sun s
H. A., which equals 8 h , and draw PS m , the hour circle of the mean sun. We see
from the figure that the hour angle of the mean sun from Greenwich (G. M. T.) is
equal to 24 h (Long. + H. A. SjJ , and that, since the mean sun must travel around
the arc to the west from S m to G to make the time hours on April 22 at
TIME AND THE NAUTICAL ALMANAC.
113
FIG. 40.
Greenwich, the date must be April 21, and the G. M. T. is 11 hours. For this
Greenwich date, we get, from the Nautical Almanac (corrected for G. M. T.) the
R. A. M. S. equal to l h 58 m 42 8 .2, which is the amount the hour circle of the mean
sun is to the eastward of the hour circle of the Vernal Equinox. The correction is +
or additive for the reason given in the preceding example. Lay off the arc S m V
equal to the R. A. M. S. and draw the hour circle of the Vernal Equinox PV.
An inspection of the figure shows us that the L. S. T. is the arc QGV which is equal
to the Long. + G. M. T. + R. A. M. S., or to the L. M. T. + the R. A. M. S. We
also see that L. M. T. equals the Long, -f G. M. T.
FIRST EXAMPLE OF ARTICLE 291. (SEE FIGURE 40.)
Draw the figure as shown, laying off the longitude
equal to 5 hours east, to the westward from Q, thus
finding the Greenwich meridian G. The given L. S. T.
is 18 hours, so lay off QV (equal to 18 hours) to the
westward from Q, given the position of V, the Vernal
Equinox or First roint of Aries, for the instant de
sired. The problem is to plot the position of the
mean sun at this hist ant, and thence find its local
hour angle, or the L. M. T. We plot this position of
the mean sun by laying off its right ascension to
the eastward from V. The R. A. M. S. is found from
the Almanac for a particular instant which is at
Greenwich mean noon of the astronomical date,
April 21, and which we find is l h 56 m 53 s . 8. Plot in S mi , over the Greenwich merid
ian and lay off this angle GV 17 to the westward from G, giving us the position of V
at Greenwich mean noon. As we are reckoning hour angles from the local meridian,
we must move the sun back to Q and find the position \ 3 at the instant of local mean
noon. To find V 2 we must find the angle Q V 3 which will be less than GV t , as the
First Point of Aries always advances faster toward the west than the mean sun.
The amount of this gain of the Vernal Equinox over the mean sun depends on the
angular distance through which the mean sun travels, i. e., hi this case from Q to G
equals the longitude, equals 5 hours. From Table 9 we find the gain, which is
represented by the sector Q in the figure, to be 49 s . 3 for the 5 hours, so that QV 2
equals GV l - 49 S .3^ equals l h 56 m 53 8 .8 - 49 8 .3, eauals l h 56 m 04 3 .5. Now we
have the position V 2 for the instant of tune when tne mean sun was at Q, that is
for the position S m2 or local mean noon. For the instant of time desired the Vernal
Equinox is not at V 2 but at V and at this instant we must find S m2 . The Vernal
Equinox has moved from V 2 to the westward to V or through the arc V 2 V which
equals QV r QV 2 , equals 17 h 58 m 42 8 .2-l h 56 m 04 8 .5, equals 16 h 02 m 37 8 .7, which
is called a sidereal interval. During this travel of the
Vernal Equinox the mean sun will lose a certain an
gular amount on the Vernal Equinox, depending on
the travel of the latter, which travel is 16 h 02 m 37 8 .7.
From Table 8, we find for this travel that the loss
will be 2 m 37 8 .7, which is represented by the sector
C 2 in the figure, so that the angle QS m is V 2 V-2 m
37 S .7, equals 16 h 02 m 37 8 .7-2 m 37 8 .7, equals 16 h
00 m 00 s , which, from the figure, equals the aesired L.
M. T.
SECOND EXAMPLE OF ARTICLE 291 . (SEE FIGURE 41 .)
Draw the figure as shown, laying off the longitude
equal to 5 h west, to the eastward from Q, thus finding
the Greenwich meridian G. The problem is similar
to the above problem except that in moving the mean FIQ. 41.
sun from G to Q we see that the angle S mi V l is in
creased to find S m2 V 2 , as the Vernal Equinox has gained a certain amount on the
mean sun during the travel of the sun to the westward from G to Q. For the travel
of V 2 to V, the mean sun will travel from S m2 to S m , losing a certain amount on the
Vernal Equinox for the travel of V 3 V of the latter, and we find QS m equals the L. M. T.
114
TIME AND THE NAUTICAL ALMANAC.
FIRST EXAMPLE OF ARTICLE 293. (SEE FIGURE 42.)
Draw the figure as explained above, using longitude given equals 5 hours west,
and L. M. T. given, 12 hours ( + ). Then G. M. T. equals 12 + 5 or 17 hours (+ ) of
April 25. For this instant of time the mean sun is plotted at S m .
Now the problem is, knowing the positions of G, Q,
and S m , to find the position of the given star on the di
agram, and thence its local hour angle. If we can find
the relative angles from the mean sun and from the
star to some third object, we can plot this third object
and find the required hour angle of the star. The third
object is the First Point of Aries (the Vernal Equinox)
and the angles from the mean sun and from the star
are the right ascensions of the mean sun and the star.
The right ascension of the mean sun is found from the
Almanac, not for the instant we want, but for the
Greenwich mean noon of the date. This R. A. must
be increased by a correction for the angle through
which the mean sun has traveled since noon, the
G. M. T. In the problem the R. A. M. S. so increased
is 2 hours, so we lay^ off S m V from S m to the westward
2 hours, plotting the position of the Vernal Equinox at the desired instant. From
the Almanac we find the R. A. of the star to be 6 hours, and we lay; off V * equal
to 6 hours to the eastward. The required local hour
angle of the star is then Q ^c which equals QS m +
VS m -V * equals L. M. T. + R. A. M. S.-R. A. equals
12 h +2 h -6 h equals 8 hours.
SECOND EXAMPLE OF ARTICLE 293. (SEE FIGURE 43.)
Draw the figure as before. The problem is, know
ing the position of the star at a certain instant, to find
the L. S. T., so we must plot the position of the star,
then that of the Vernal Equinox. The local hour angle
of the latter is the required L. S. T.
The hour angle 01 the star is given as 2 hours, bear
ing east from the meridian, so lay off Q ^c =2 hours to
the east from Q. Now find from the Almanac the R. A.
of the ^ which is 14 hours, and lay off >fc V equal to 14 h to
the westward from % . The L. S. T. is then QV, equals
V * Q *, equals the R. A. * II. A. *, equals 14 h 2 h equals 12 hours.
When doubt exists as to the Greenwich date the navigator, by plotting the data
in exactly the same way as explained above, can at once remove all doubt on the
subject and can get the correct G. M. T.
CHAPTER X.
COKRECTION OF OBSERVED ALTITUDES,
294. The true altitude of a heavenly body at any place on the earth s surface
is the altitude of its center, as it would be measured by an observer at the center of
the earth, above the plane passed through the center of the earth at right angles
to the direction of the zenith.
The observed altitude of a heavenly body, as measured at sea, may be converted
to the true altitude by the application of the following-named corrections: Index
Correction, Dip, Refraction, Parallax, and Semidiameter. The corrections for parallax
and semidiameter are of inappreciable magnitude in observations of the fixed stars,
and with planets are so small that they need only be regarded in refined calculations.
In observations with the artificial horizon there is no correction for dip.
For theoretical accuracy, the corrections should be applied in the order in which
they are named, but in ordinary nautical practice the order of application makes
no material difference, except in the case of the parallax of the moon as explained
in article 306 ; and hence, instead of turning to the separate tables referred to in the
following articles as containing these corrections, their combined amount, given in
Table 46, may be applied to observed altitudes of the sun, the planets, and the stars,
after the manner shown in article 308.
INDEX CORRECTION.
295. This correction is fully explained in articles 249 and 250, Chapter VIIL
REFRACTION.
296. It is known by various experiments that the rays of light deviate from
their rectilinear course in passing obliquely from one medium into another bf a
different density; if the latter be more
dense, the ray will be bent toward the per
pendicular to the line of junction of the
media; if less dense, it will be bent away
from that perpendicular.
The ray of light before entering the
second medium is called the incident ray;
after it enters the second medium it is
called the refracted ray, and the difference of
direction of the two is called the refraction.
The rays of light from a heavenly body
must pass through the atmosphere before
reaching the eye of an observer upon the
surface of the earth. The earth s atmos
phere is not of a uniform density, but is
most dense near the earth s surface, gradu
ally decreasing in density toward its upper
limit; hence the path of a ray of light, by
passing from a rarer medium into one con
tinually increasing density becomes a curve,
which is concave toward the earth. The
last direction of the ray is that of a tangent to the curved path at the eye of the
observer, and the difference of the direction of the ray before entering the atmosphere
and this last direction constitutes the refraction.
297. To illustrate this, consider the earth s atmosphere as shown in figure 44;
let SB be a ray from a star S, entering the atmosphere at B, and bent into the curve
BA; then the apparent direction of the star is AS , the tangent to the curve at the
point A, the refraction being the angle between the lines BS and AS . If CAZ is
115
FIG. 44.
116
CORRECTION OF OBSERVED ALTITUDES.
the vertical line of the observer, by a law of optics the vertical plane of the observer
which contains the tangent AS must also contain the whole curve BA and the incident
ray BS. Hence refraction increases the apparent altitude of a star without affecting
its azimuth.
At the zenith the refraction is nothing. The less the altitude the more obliquely
the rays enter the atmosphere and the greater will be the refraction. At the horizon
the refraction is the greatest.
298. The refraction for a mean state of the atmosphere (barometer 30 in , Fahr.
thermometer 50) is given in Table 20 A; the combined refraction and sun s parallax
in Table 20 B; and the combined refraction and moon s parallax in Table 24.
Since the amount of the refraction depends upon the density of the atmosphere,
and the density varies with the pressure and the temperature, which are indicated
by the barometer and thermometer, the true refraction is found by applying to the
mean refraction the corrections to be found in Tables 21 and 22; these are deduced
from BesseFs formulae, and are regarded as the most reliable tables constructed. It
should be remembered, however, that under certain conditions of the atmosphere a
very extraordinary deflection occurs in rays of light which reach the observer s eye
from low altitudes (that is, from points near the visible horizon), the amount of
which is not covered by the ordinary corrections for pressure and temperature ; the
error thus created is discussed under Dip (art. 301) ; on account of it, altitudes less
than 10 should be avoided.
EXAMPLE: Required the refraction for the apparent altitude 5, when the thermometer is at 20
and the barometer at 30 in .67.
The mean refraction by Table 20 A is, 9 52"
The correction for height of barometer is, -f- 13
The correction for the temperature, -f 42
True refraction, 10 47
299. The correction for refraction should always be subtracted, as also that
for combined refraction and parallax of the sun; the correction for combined refrac
tion and parallax of the moon is invariably additive.
DIP.
300. Dip of the Horizon is the angle of depression of the visible sea horizon below
the true horizon, due to the elevation of the eye of the observer above the level of
the sea.
In figure 45 suppose A to be the position of an observer whose height above the
level of the sea is AB. CAZ is the true vertical at the position of the observer, and
AH is the direction of the true horizon, S
being an observed heavenly body. Draw
ATH tangent to the earth s surface at T.
Disregarding refraction, T will be the most
distant point visible from A. Owing to
refraction, however, the most distant visi
ble point of the earth s surface is more re
mote from the observer than the point T,
and is to be found at a point T , in figure
46. But to an observer at A the point T
will appear to lie in the direction of AH",
the tangent at A to the curve AT . If the
verticalplane were revolved about CZ as
an axis, the line AH would generate the
plane of the true horizon, while the point
T would generate a small circle or the
terrestrial sphere called the Visible or Sea
Horizon. The Dip of the Horizon is
HAH", being the angle between the true
FIG. 43. horizon and the apparent direction of the
sea horizon. Values of the dip are given
in Table 14 for various heights of the observer s eye, and in the calculation of the
table allowance has been made for the effect of atmospheric refraction as it exists
under normal conditions.
CORRECTION OF OBSERVED ALTITUDES.
117
FIG. 46.
301. The fact must be emphasized, however, that under certain conditions the
deflection of the rav in its path from the horizon to the eye is so irregular as to give a
value of the dip widely different from that which is tabulated for the mean state of
atmosphere. These irregularities usually occur when there exists a material differ
ence between the temperature of the sea water and that of the air, and they attain a
maximum value in calm or nearly calm weather, when the lack of circulation permits
the air to arrange itself in a series of horizontal strata of different densities, the denser
strata being below when the air is warmer, and the reverse condition obtaining when
the air is cooler. The effect of such an arrangement is that a ray of light from the
horizon in passing through media of different densities, undergoes a refraction quite
unlike that whicn occurs in the atmosphere of much more nearly homogeneous
density that exists under normal conditions.
Various methods have been suggested for computing the amount of dip for
different relative values of temperature of air and water, but none of these afford a
satisfactory solution, there being so many ele
ments involved which are not susceptible of
determination by an observer on shipboard
that it will always be difficult to arrive at
results that may be depended upon.
As the amount of difference between the
actual and tabulated values of the dip due to
this cause may sometimes be very consider
able reliable observations having frequently
placed it above 10 , and values as high as 32
having been recorded it is necessary for the
navigator to be on his guard against the
errors thus produced, and to recognize the
possible inaccuracy of all results derived from
observations taken under unfavorable condi
tions. Without attempting to give any method
for the determination of the amount of the ex
traordinary variation in dip, the following rules may indicate to the navigator the con
ditions under which caution must be observed, and the direction of probable error:
(a) A displacement of the horizon should always be suspected when there is a
marked difference between the temperatures of air and sea water; this fact should
be especially kept in mind in regions such as those of the Red Sea and the Gulf
Stream, where the difference frequently exists.
(6) The error In the tabulated value of the dip will increase with an increase in the
difference of temperature, and will diminish with an increase in the force of the wind.
(c) The error will decrease with the height of the observers eye; hence it is
expedient, especially when error is suspected, to make the observation from the most
elevated position available.
(d) When the sea water is colder than the air the visible horizon is raised and the
dip is decreased; therefore the true altitude is greater than that given by the use of
the ordinary dip table. When the water is warmer than the air, the horizon is
depressed and the dip is increased. At such times the altitude is really less than that
found from the use of the table.
The same cause, it may be mentioned here, affects the kindred matter of the
visibility of objects. When the air is warmer, terrestrial objects are sighted from a
greater distance and appear higher above the horizon than under ordinary conditions.
When the water is warmer than the air, the distance of visibility is reduced, and
terrestrial objects appear at a less altitude.
302. What has peen said heretofore about the dip supposes the horizon to be
free from all intervening land or other objects; but it often nappens that an obser
vation is required to be taken from a ship sailing along shore or at anchor in harbor,
when the sun is over the land and the snore is nearer the ship than the visible sea
horizon would be if it were unconfined; in this case the dip will be different from
that of Table 14, and will be greater the nearer the ship is to that point of the shore
to which the sun s image is brought down. In such case Table 15 gives the dip at
different heights of the eye and at different distances of the ship from the land.
303. The dip is always to be subtracted from the observed altitude.
118
CORRECTION OF OBSERVED ALTITUDES.
PARALLAX.
304. The parallax of a heavenly body is, in general terms, the angle between
two straight lines drawn to the body from different points. But in Nautical Astron
omy geocentric parallax is alone considered, this
being the difference between the positions of a
heavenly body as seen at the same instant from
the center of the earth and from a point on
its surface.
The zenith distance of a body, S (fig. 47),
seen from A, on the surface of the earth, is ZAS;
seen from C it is ZCS; the parallax is the dif
ference of these angles, ZAS-ZCS=ASC.
Parallax in altitude is, then, the angle at
the heavenly body subtended by the radius
of the earth.
If the heavenly body is hi the horizon as
at II , the radius, being at right angles to AH ,
subtends the greatest possible angle at the
star for the same distance, and this angle is
called the horizontal parallax. The parallax
is less as the bodies are farther from the earth,
as will be evident from the figure.
FIG. 47.
Let par. = parallax in altitude, ASC;
Z=SAZ, the apparent zenith distance (corrected for refraction);
R=AC, the radius of the earth; and
D = CS, the distance of the object from the center of the earth.
Then, since SAC = 180-SAZ, the triangle ASC gives:
R sin Z
sin par. = ^ .
If the object is in the horizon at H , the angle AH C is the horizontal parallax,
and denoting it by H. P. the right triangle AH C gives:
sin H. P.
R
R.
Substituting this value of ^ in the above,
sin par. = sin H. P. sin Z.
If A- = SAH , the apparent altitude of the heavenly body, then Z = 90 7i; hence,
sin par. = sin H. P. cos 7i.
Since par. and H. P. are always small, the shies are nearly proportional to the
angles; hence,
par. = H. P. cos 7i.
305. The Nautical Almanac gives the horizontal parallax of the moon, as well
as .of the planets Venus, Mars, Jupiter, and Saturn.
In Table 16 will be found the values of the sun s parallax for altitude intervals
of 5 or 10, while Table 20 B contains the combinea values of the sun s parallax
and the refraction. In Table 24 is given the parallax of the moon, combined with
the refraction, at various altitudes and for various values of the horizontal parallax.
CORRECTION OF OBSERVED ALTITUDES. 119
306. Parallax is always additive; combined parallax and refraction additive in
the case of the moon, but subtractive for the sun.
As the correction for parallax of the moon is so large, it is essential that it be
taken from the table with considerable accuracy; the corrections for index correc
tion, semidiameter, and dip should therefore be applied first, and the l approximate
altitude" thus obtained should be used as an argument in entering Table 24 for
parallax and refraction.
SEMIDIAMETEB.
307. The semidiameter of a heavenly body is half the angle subtended by the
diameter of the visible disk at the eye of the observer. For the same body the
semidiameter varies with the distance; thus ; the difference of the sun s semidiameter
at different times of the year is due to the change of the earth s distance from the
sun; and similarly for the moon and the planets.
In the case 01 the moon, the earth s radius bears an appreciable and considerable
ratio to the moon s distance from the center of the earth; hence the moon is materially
nearer to an observer when in or near his zenith than when in or near his horizon,
and therefore the semidiameter, besides having a menstrual change, has a semi
diurnal one also.
The increase of the moon s semidiameter due to increase of altitude is called its
augmentation. This reduction may be taken from Table 18.
The scmidiameters of the sun, moon, and planets are given in their appropriate
places in the Nautical Almanac.
The semidiameter is to be added to the observed altitude in case the lower limb
of the body is brought into contact with the horizon, and to be subtracted in the
case of ^ the upper limb. When the artificial horizon is used, the limb of the reflected
image is that which determines the sign of this correction, it being additive for the
lower and subtractive for the upper.
EXAMPLE: May 6, 1916, the observed altitude of the sun s upper limb was 62 1(X 40"; I. C., -f 3 10";
height of the eye, 25 feet. Required the true altitude.
Obs. alt. & 62 1(X 40" I. C., + 3 10"
Corr., - 18 04
S. D. (Naut. Aim.), - 15 53"
True alt., 61 52 36 dip (Tab. 14), - 4 54
p. &r. (Tab. 20 B), - 27
- 21 14
Corr., - 18 04 X/
EXAMPLE : The altitude of Sirius aa observed with an artificial horizon was 50 59 30"; I. C. , V 30".
Required the true altitude.
Obs. 2 alt. *, 50 59 30*
I. C., - 1 30
2)50 58 00
Obs. alt., 25 29 00
ref. (Tab. 20 A), - 2 02
True alt., 25 26 58
EXAMPLE: April 16, 1916, observed altitude of Venus 53 26 10"; I. C., + V 30"; height of eye,
20 feet. Required the true altitude.
Obs. alt. *, 53 26 10" par. (Tab. 17), + (/ 06" Hor. Par. (Naut. Aim.), 11".4
Corr., 2 30 I. C., + 2 30
53 23 40 + 2 36
dip (Tab. 14), - 4 23"
ref. (Tab. 20 A), - 43
- 5 06
Corr., - 2 30"
120 CORRECTION OF OBSERVED ALTITUDES.
EXAMPLE: May 6, 1916, at 13 h 24 m G. M. T., the observed altitude of the moon s lower limb was
25 3(X 30"; I. 0.,-1 30"; height of eye, 20 feet. Required the true altitude.
Obs. alt. j[_, 25 3(K 30" S. D. (Naut. Aim.), +14 48" Hor. Par. (Naut. Aim ) 54 06"
1st corr., + 9 01 Aug. (Tab. 18), + 06
Approx. alt., 25 39 31 +14 54
p. & r. (Tab. 24),
True alt.,
*U 1<J
dip. (Tab. 14),
i.e.,
- 4 23"
- 1 30
26 26 16
- 5 53
1st corr.,
+ 9 01"
Or, the following modification may be adopted:
Obs. alt., 25 30 30" S. D., +14 48" H. P., 3246" log. 3.51135
1st corr., -f 6 59 Aug., + 06 App. alt., 25 38 cos 9.95504
Approx. alt., 25 37 29 +14 54 f 2927" log. 3.46639
par., + 48 47 _ T1 F ^ W 47"
True alt., 26 26 16 ref, - 2 02
I. C., - 1 30
- 7 55
1st corr., + 6 59"
308. The corrections for dip, parallax, refraction, and semidiameter, which
must be applied to the observed altitude of a star or of the sun s lower limb in order
to obtain the true altitude, have been combined in Table 46, and for the moon s
upper and lower limb in Table 49, and will henceforth be used in all subsequent
problems. This is done in order to save the time and labor involved in referring
to separate tables of these corrections.
The tabulated correction for an observed altitude of a star combines the mean
refraction and the dip; and that for the observed altitude of the sun s lower limb,
the mean refraction, the dip, the parallax, and the mean semidiameter, which is
taken as 16 . A supplementary table, taking account of the variation of the sun s
semidiameter in the different months of the year, is given in connection with the
main table.
Thus, in the first example under article 324, we may, when variations from the
mean state of the atmosphere (barometer 30 inches, Fahr. thermometer 50) are
left out of consideration, proceed as follows:
Measured altitude _ } = 40 04 00"
I.C. = + 3 00
Correction from Table 46, height of eye 20 feet. +10 35" 40 07 00
Supplementary table for June 21 _ 14 10 21
True altitude 40 17 21
CHAPTER XI.
THE CHKONOMETER EEKOR
309. It has already been explained (art. 261, Chap. VIII) that the error of a
chronometer is the difference between the time indicated by it and the correct standard
time to which it is referred; and that the daily rate is the amount that it gams or
loses each day. In practice, chronometer errors are usually stated with reference to
Greenwich mean time. It is not required that either the error or the rate shall be
zero, but in order to be enabled to determine the correct time it is essential that both
rate and error be known and that the rate shall have been uniform since its last
determination.
310. DETERMINING THE RATE. Since all chronometers are subject to some
variation in rate under the changeable conditions existing on shipboard, it is desirable
to ascertain a new rate as often as possible. The process of obtaining a rate involves
the determination of the error on two different occasions separated by an interval
of time of such length as may be convenient ; the change of error during this interval,
divided by the number of days, gives the daily rate.
EXAMPLE: On March 10, at noon, found chronometer No. 576 to be O m 32V5 fast of G. M. T. ; on March
20, at noon, the same chronometer was O m 48 s .O fast of G. M. T. What was the rate?
Error, March 10 d O h , - -f O m 32 . 5
Error, March 20 d 0*, +0 48 .
Change in 10 days, -}- 15 . 5
Daily rate, + 1-.55
The chronometer is therefore gaining 1 8 .55 per day.
311. DETERMINING ERROR FROM RATE. The error on any given day being
known, together with the daily rate, to find the error on any other day it is only
necessary to multiply the rate by the number ^of days that may have elapsed and
to apply the product with proper sign to the given error.
EXAMPLE: On December 17 a chronometer is 3 m 27 s . 5 slow of G. M. T. and losing 8 .47 daily. What
is the error on December 26?
Error Dec. 17, -3 m 27 .5 Daily rate, -OV47
Correction, 4 .2 No. days, 9
Error Dec. 26, -3 31.7 Corr., -4.23
The chronometer is therefore slow of G. M. T. on December 26, 3 m 31 8 .7.
312. It is necessary to distinguish between the signs of the chronometer correc
tion and of the chronometer error. A chronometer fast of the standard time is
considered as having a positive error, since its readings are positive to (greater than)
those of an instrument showing correct tune; but the same chronometer has a
negative correction, as the amount must be subtracted to reduce chronometer readings
to correct readings.
313. Numerous methods are available for determining the error of a chronometer
in port. The principal of these will be given.
BY TIME SIGNALS.
314. In nearly all of the important ports of the world a time signal is made each
dav at some defined instant. In many cases this consists in the dropping of a time
ball the correct instant being given telegraphically from an observatory. In a
number of places where there is no tune ball a signal may be received on the instru
ments at the telegraph offices, whereby mariners may ascertain the errors of their
chronometers. Such signals are to be had in almost every port of the United States,
and similar signals are being sent out from Government radio stations, so that
it is now possible to find the error of the chronometer on board ships fitted with
121
122 THE CHRONOMETER ERROR.
receiving instruments when lying in port and also when underway within radio
distance of these stations.
The time signal may be given by a gunfire or other sound, in which case allowance
must be made by the observer for the length of time necessary for the sound to travel
from the point of origin to his position. Sound travels 1,090 feet per second at 32 F.,
and its velocity increases at the rate of 1.15 feet per second with each degree increase
of temperature. If V be the velocity of sound in feet per second at the existing
temperature, and D the distance in feet to be traversed, is the number of seconds
to be subtracted from the chronometer reading at the instant of hearing the signal
to ascertain the reading at the instant the signal was made.
This method of obtaining the chronometer error consists in taking the difference
between the standard time and chronometer time at the time of observation and
marking the result with appropriate sign.
EXAMPLE: A time ball drops at 5 h O m s , G. M. T., and the reading of a chronometer at the same
moment is 4 h 57 m 52 3 .5. What is the chronometer error?
G. M. T., 5 h OO m OO I
Chro. t., 4 57 52.5
Chro. error, - 2 07 . 5
That is, chronometer is slow 2 m 07". 5; chronometer correction additive.
BY TRANSITS.
315. The most accurate method of finding the chronometer correction is by
means of a transit instrument well adjusted in the meridian, noting the times of
transit of a star or the limbs of the sun across the threads of the instrument.
At the instant of the body s passage over the meridian wire, mark the time by
the chronometer. The hour angle at the instant is O h ; therefore the local sidereal
time is equal to the right ascension of the body in the case of a star, or the local
apparent time is O h in the case of the sun s center. By converting this sidereal or
apparent time into the corresponding mean time and applying the longitude, the
Greenwich mean time of transit is given. By comparing with this the time shown
by chronometer the error is found.
EXAMPLE: 1916, May 9 (Ast. day), in Long. 44 39 E., observed the transit of Arcturus over the
middle wire of the telescope, the time noted by a chronometer regulated to Greenwich mean time being
8 h 05 m 33 s . 5. Required the error.
L. S. T. (R. A. #), 14 h ll m 52 8 .9
Long., 2 58 36
G. S. T., 11 13 16.9
R. A. M. S., 9 d O h , - 3 07 51.8
Sid. int. from O h , 8 05 25.1
Reduction (Tab. 8), - 1 19.5
G. M. T., 8 04 05.6
Chro. t., 8 05 33.5
Chro. fast, 1 27 . 9
EXAMPLE: June 25, 1916, in Long. 60 E., observed the transit of both limbs of the sun over the
meridian wire of the telescope, noting the times by a chronometer. Find the error of the chronometer
onG.M. T.
Transit of western limb, 8 h 04 m 02 s . 5 Eq. t., 24 d 20*., 2 m 19 s . 1
Transit of eastern limb, 8 06 20 . Add to apparent time.
Chro. time, loc. app. noon, 8 05 11 . 25
L. A. T., loc. app. noon, O b 00 m 00 s
Eq. t., + 2 19.1
L. M. T., loc. app. noon, 02 19 . 1
Long., - 4 00 00
G. M. T., loc. app. noon, 8 02 19.1
Chro. time, loc. app. noon, 8 05 11 . 25
Chro. fast, 2 52 . 15
THE CHRONOMETER ERROR.
123
BY A SINGLE ALTITUDE (TIME SIGHT).
I. The problem involved in this solution, by reason of its frequent application
mining the longitude at sea, is one of the most important ones in Nautical
316,
in determining
Astronomy. It consists in finding the hour angle from given values of the altitude,
latitude, and polar distance. The hour angle thus obtained is converted by means
of the longitude and equation of time in the case of the sun, or longitude and right
ascension in the case of other celestial bodies, into Greenwich mean time; and this,
compared with the chronometer time, gives the error.
317. It should be borne in mind that the most favorable position of the heavenly
body for time observations is when near to the prime vertical. When exactly in
the prime vertical a small error in the latitude produces no appreciable effect.
Therefore, if the latitude is uncertain, good results may be obtained by observing the
sun or other body when bearing east or west. If observations are made at the same
or nearly the same altitude on each side of the meridian and the mean of the results
is taken, various errors are eliminated of which it is otherwise impossible to take
account, and a very accurate determination is thus afforded.
318. With a sextant and artificial horizon or good sea horizon, several altitudes
of a body should be observed in quick succession, noting in each case the time as shown
by a hack chronometer or comparing watch whose error upon the standard chronom
eter is known. Condensing the observation into a brief interval justifies the assump
tion that the altitude varies uniformly with the time. A very satisfactory method
is to set the sextant in advance at definite intervals of altitude and note the time as
contact is observed.
319. Correct the observed altitude for instrumental and other errors, reducing
the apparent to the true altitude.
If the sun, the moon, or a planet is observed, the declination is to be taken from
the Nautical Almanac for the time of the observation. If the chronometer correction
is not approximately known and it is therefore impossible to determine the Greenwich
mean time of observation with a fair degree of accuracy, the first hour angle found
will be an approximate one ; the declination corrected by this new value of the tune
will produce a more exact value of the hour angle, and the operation may be repeated
until a sufficiently precise value is determined.
320. In figures 48 and 49 are given:
AM =7i, the altitude of the body M;
DM = d, the declination ; and
Q Z = L, the latitude of the place.
In the astronomical triangle PMZ there may be found from the foregoing:
= z, the zenith distance of the body, = 90 Ji;
124
THE CHKONOMETER ERROR.
PM = p, the polar distance, = 90 d; and
PZ =co.L, the co-latitude of the place, = 90 L.
From these data it is required to find the angle MPZ the hour angle of the
body, =t. This is given by the formula:
snr 5 * t =
cos L sin p
If we let s = J
this becomes:
sin J t = ^/sec L cosec p cos s sin (s 7i).
The polar distance is obtained by adding the declination to 90 when of different
name from the latitude and subtracting it from 90 when of the same name. Like
latitude and altitude, it is always positive.
If the sun is the body observed, the resulting hour angle is the local apparent
time and is to be taken from the a. m. or p. m. column of Table 44 according as the
altitude is observed in the forenoon or afternoon. If the moon, a star, or a planet
be taken, the hour angle is always found in the p. m. column.
Local apparent time as deduced from an observation of the sun is converted to
local mean time by the application of the equation of time; then, by adding the
longitude if west and subtracting it if east, the Greenwich mean time is obtained.
The hour angle of any other body, added to its right ascension when it is west of
the meridian at observation or subtracted therefrom when east, gives the local sidereal
time, which may be reduced to Greenwich sidereal time by the application of the
longitude, and thence to Greenwich mean time by methods previously explained.
A comparison of the Greenwich mean time with the chronometer time of sight
gives the error of the chronometer.
EXAMPLE: January 20, 1916, p. m., in Lat. 48 4V 00" S., Long. 69 03 00" E., observed a series
of altitudes of the sun with a sextant and artificial horizon; mean double altitude, 59 03 10", images
approaching; mean of times by comparing watch, 4 h 40 m 56 s ; C W, 7 h 23 m 25 s ; index correction, - V 30";
approximate chronometer correction, O m 10 s . What was the exact chronometer error?
W. T.. 4h
C W, 7
40> 56s Obs. 2 alt. Q 59 03 10"
23 25 I.C., 1 30
Dec. Oh.,
20 20 .8 S.
Eq. t. Oh, 10" 5K7
H. D., + Qs.7
G. M. T., Qh.07
Chro. t.,
04 21
10
2)59 01 40
G. M. T.,
Corr
Oh.07
App. . .,
29 30 50
+ 14 43
ft 03 <?
Corr., + 0".049
Eq. t., Oh 4* 11", 10m sie.8
(Add to apparent time.)
4 h 30 m 40 8 . 4
+ 10 51.8
App. G. M. T.,
1
L
P
s
sh
L. A
04 11 g)rr.,
ft,
S.D.,
p. & r.,
Corr.,
29 45 33"
48 41 00
69 39 14
Dec.,
18031
02798
43906
84403
20 20 46" S.
69 39 14"
L. A. T.,
Eq. t.,
L. M. T.,
Long.,
G. M. T.,
Chro. t.,
Chro. slow,
29 45 33
+ 16 17"
- 1 34"
+ 14 43"
sec
cosec
cos 9.
sin 9.
4 41 32.2
-4 36 12 .
2)148 05 47
74 02 54
44 17 21
. T., 4 h 30 m 40 8 .4
05 20.2
04 21.0
2)19.
49138
00 59.2
sin | t 9.
74569
THE CHRONOMETER ERROR.
125
EXAMPLE: May 18, 1916, p. m., in Lat. 8 03 22" S., Long. 34 51 57" W., observed a series of
altitudes of the star Arcturus. east of the meridian, using artificial horizon; mean double altitude,
60 KK; mean watch time, 6 h 50 32 s ; C W, 2 h 20 59V5; I. C., +2 00". Find the true error of the
chronometer.
N.
W. T.,
r 1 w
6
2
50 m
20
32 s
59.5
Obs. 2 alt. #, 60
I. C., +
1(X 00"
2 00
R. A. :
*:, 14 h ll m 52.9
Dec. #, 19 36
/ 54 //
Chro. t., 9
h 30
L 8
p 109
11
04
03
36
31.5
20"
22
54
2)60
12 00
P,
109 36
14 h llnl
- 3 36
/ 54 //
52 s . 9
01.3
30
ref.,
06 00
1 40
h, 30
sec . 00431
cosec . 02596
cos 9. 44372
sin 9. 84019
04 20
R. A. #,
H. A.,
L. S. T.,
Long.,
G. S. T.,
R. A. M. S., 0",
Sid. int. from O 11 ,
Red. (Tab. 8),
G. M. T.,
Chro. t.,
10
+ 2
35
19
51.
27.
6
8
I
s-h
H.A.,
2)147
44
36
73 52
43 47
3 h 36 m 01
18
58
.3E.
12
- 3
55
43
19 .
20.
4
8
2)19. 31418
9
11
1
58.
30.
6
4
sin * t 9. 65709
9
9
10
11
28.
31.
2
5
Chro. fast,
1 03.3
BY DOUBLE ALTITUDES OB ALTITUDES ON OPPOSITE SIDES OF THE MEBEDIAN.
320. Instead of relying on a single determination of the chronometer error from
altitudes on one side of the meridian, it is better to observe the same body on both
sides of the meridian, and, if possible, at about the same altitude. The error of the
chronometer having been found from each set of sights, the mean is taken as the
correct error, and this mean will probably be nearer the true error than the result
from either set, the effect of the constant errors of latitude, instrument, and observer,
being opposite in the two cases, will be eliminated by taking the mean.
CHAPTER XII.
LATITUDE,
BY MERIDIAN ALTITUDE.
321. The latitude of a place on the surface of the earth, being its angular
distance from the equator, is measured by an arc of the meridian between the zenith
and the equator, and hence is equal to the declination of the zenith; therefore, if the
zenith distance of any heavenly body when on the meridian be known, together with
the declination of the body, the latitude can be found.
Let figure 50 represent a projection of the celestial sphere on the plane of the
meridian NZS; O, the center of the sphere; NS, the horizon; P and P , the poles of
the sphere; QOQ , the equator; Z, the zenith of the
observer. Then, by the above definition, ZQ will
be the latitude of the observer; and NP, the altitude
of the elevated pole, will also equal the latitude.
Let M be the position of a heavenly body north
of the equator, but south of the zenith; QM = d, its
declination^ MS = /i, its altitude; and ZM = z = 90
Jij its zenith distance.
From the figure we have:
QZ = QM+MZ, or
FIG. 50.
By attending to the names of z and d, marking
the zenith distance north or south according as the
zenith is north or south of the body, the above
equation may be considered general for any position of the body at upper transit,
asM, M , M".
In case the body is below the pole, as at M" that is, at its lower culmination
the same formula may be used by substituting 180 d for d. Another solution is
given in this case by observing that:
NP=PM "
or
322. A^common practice at sea is to commence observing the altitude of the
sun s lower limb above the sea horizon about 10 minutes before noon, and then, by
moving the tangent-screw, to follow the sun as long as it rises; as soon as the highest
altitude is reached, the sun begins to fall and the lower limb will appear to dip.
When the sun dips the reading of the limb is taken, and this is regarded as the
meridian observation.
It will, however, be found more convenient, and frequently more accurate, for
the observer to have his watch set for the local apparent time of the prospective noon
longitude, or to know the error of the watch thereon, and to regard as the meridian
altitude that one which is observed when the watch indicates noon. This will save
time and try the patience less, for when the sun transits at a low altitude it may
remain "on a stand," without appreciable decrease of altitude for several minutes
after noon; moreover, this method contributes to accuracy, for when the conditions
are such that the motion in altitude due to change of hour angle is a slow one, the
motion therein due to change of the observer s latitude may be very material, and
thus have considerable influence on the time of the sun s dipping. This error is large
enough to take account of in a fast-moving vessel making a course in which there is a
good deal of northing or southing.
LATITUDE. 127
In observing the altitude of any other heavenly body than the sun, the watch
time of transit should previously be computed and the meridian altitude taken by
time rather than by the dip. This is especially important with the moon, whose
rapid motion in decimation may introduce still another element of inaccuracy.
323. The watch time of transit for the sun, or other heavenly body, may be
found by the forms given below, knowing the prospective longitude, the chronometer
error, and the amount that the watch is slow of the chronometer. In this connection,
article 404 describing the method of setting the watch to L. A. T. may be
profitably read.
For the Sun. For other Bodies.
h m
L. A. T. noon, O h 00 m 00* L. S. T. transit, (Right ascension.)
Long. (+ if west), Long, (-{-if west), dt
G. A. T., G. S. T.,
Eq. t., R. A. M. S.,0 11 , -
G. M. T., Sid int. from O 11 ,
C. C. (sign reversed), T Red. (Tab. 8), -
Chro. time, G. M. T.,
O W, - C. C. (sign reversed), T
Watch time noon, Chro. time,
C W, -
Watch time transit,
324. From the observed altitude deduce the true altitude, and thence the true
zenith distance. Mark the zenith distance North if the zenith is north of the body
when on the meridian, South if the zenith is south of the body.
Take out the declination of the body from the Nautical Almanac for the time
of meridian passage, having regard for its proper sign or name.
The algebraic sum of the decimation and zenith distance will be the latitude.
Therefore, add together the zenith distance and the declination if they are of the
j same name, but take their difference if of opposite names; this sum or difference
i will be the latitude, which will be of the same name as the greater.
EXAMPLE: At sea, June 21, 1916, in Long. 60 W., the observed meridian altitude of the sun s lower
limb was 40 4 ; sun bearing south; I. C.,+3 0"; height of the eye, 20 feet; required the latitude.
Obs. alt., 40 04 00" (Tab. 46), +10 21" Dec., 23 27M N. G. A. T., 4* 00* 00-
Corr., + 13 21 I. C., + 3 00 Eq. t., 1 31 .7
H. D., .0
ft, 40 17 21 Corr., +13 21" G. M. T., 4 01 31 .7
z, 49 42 39" N. Eq. t., 4* 1m 31-.7
*, (Add to app. time.)
L, 73 09 45 N.
EXAMPLE: At sea, April 14, 1916, in Long. 140 E., the observed meridian altitude of the sun s lower
limb was 81 15 30"; sun bearing north; I. C.,-2 30"; height of the eye, 20 feet.
Obs. alt.. 81 15 30" (Tab. 46), +11 30" Dec., 13* 14*, 9 14 .4 N. G. A. T.. 13<* 14^ 40> 00" Eq. t., 13<i 14>>, 0" 26.6
Corr., + 9 00 I. C., - 2 30 Eq. t., + 26 .2 Corr., .4
H. D., + O .J
ft, 81 2430 Corr., + 9 00" G. M. T., 0*>.67 G.M.T., 13 14 40 26.2 Eq.t.,13<i 14h40 c ,0 26.2
- O OO OtF O . WU. i . j T <J . \JW H . 1 . , " U 8 . D
d, 9 15 00 N. Int., 0^7
L, 39 30 N. Corr., - (K42
EXAMPLE: At sea, May 15, 1916, in Long. 0, the observed meridian altitude of the sun s lower
limb was 30 13 10"; sun bearing north; I. C.,+1 30"; height of the eye, 15 feet.
Obs. alt., 30 13 10" (Tab. 46), +10 32" Dec., 14<i 22*, 18 50 .2 N. G. A. T., Oh 00"> 00"
Corr., + 12 02 I. C., +1 30 Eq. t., 3 47 .5
H. D., + .6
30 25 12 Corr., +12 02 G. M. T., 1^.94 G. M. T., 14d 23* 56* 12.5
Corr.,
Dec.,
59 34 48" S. Corr.,
18 51 24 N.
40 43 24 S.
128 LATITUDE.
EXAMPLE: January 1, 1916, the observed meridian altitude of Siriua was 53 23 40", bearing south-
I. C.,+5 0"; height of the eye, 17 feet.
Obs. alt., 53 23 40" (Tab. 46)-4 / 45" Dec. *, 16 36 00" S.
Corr., + _ 15 I. C. +5 00
h, 53 23 55 Corr. +0 15"
2, 36 36 05" N.
d 16 36 00 S.
L, 20 00 05 N.
EXAMPLE: June 13, 1916, in Long. 65 W., and in a high northern latitude, the meridian altitude of
the sun s lower limb was 8 16 10" below the pole; height of the eye, 20 feet; I. C., CK 00".
Greenwich apparent time of lower culmination, June 13, 16 h 20 m (=Long.+12 h ).
Obs. alt., 8 16 10" (Tab. 46), + 5 11" G. A. T.,-16 h 20 m 00
Corr., 5 11 Eq. t., 04. 3
A, 8 21 21 Dec - 16h 23 15/1N " G.M.T.,16>19-55-.7
H D 4. // 1
n Q1 QQ QQ" Q ) \ v *
z, 01 oo oy o. rj. M T nb ^
180-d, 156 44 52 N. " M r T M _ "^
L, 75 06 13 N. Oorr " + Q// - 03
Alternative method. Dec., 23 15 08" N.
r oo 91 / 9 1 // _-
; ( 66 44 52 P, 66 ^ 52"
L, 75 06 13 N. 180 - rf 156 44 52" N.
EXAMPLE: July 10, 1916, in Long. 80 W., the observed meridian altitude of the moon s upper limb
was 59 6 X 40", bearing north; I. C., +2 X 0"; height of the eye, 19 feet.
Obs. alt., 59 06 X 40" (Tab. 49), + 9 7 30" G. M. T., of Gr. transit 7 h 40 m
Corr., + 11 30 I. C., + 2 00 Corr. for Long. (Tab. 11),+ 13
h, 59 18 10 Corr., + IV 30" L. M. T. local transit, 7 53
30 41 50 S. Hor Par 59 , 12/ , L ng " +_5_20_
d, 22 40 42 S. G. M. T., local transit, 13 h 13 m
L, 53 22 32 S. Dec 12h 22 o 30/ 4 g H. D., ~ 8/5
Corr., 10.3 G. M. T., l h .22
Dec., 22 40 X .7 S. Corr., - lO^S
was 51
EXAMPLE: At sea, September 16, 1916, in Long. 75 E., the observed meridian altitude of Jupiter
51 25 7 24", bearing north; I. C.,+3< 0"; height of the eye, 16 feet.
Obs. alt., 51 25 24" (Tab. 46),- 4 / 42" G. M. T., Gr. transit, 14 h
Corr., 1 42 I. C., + 300 Corr. for Long.,
ft, 51 23 42 Corr., - 1 42" L.M.T., of local transit, 14
2,
d,
38 36 18 S.
~ 5
11 38 54 N. G.M.T. of local transit, 9 29
26 57 24 S - Dec. O h , 11 39 r .5 N. H. D.,
Coir., - _ .6^ G. M. T.,
Dec., 11 38 7 .9 N. Corr., -37"=.6 X
325. CONSTANT. In working a meridian altitude, especially the daily nooni
observation of the sun, it is frequently a convenience to arrange the terms so that
aD computation, excepting the application of the observed altitude, is completed 1
beforehand; then the ship s latitude will be known immediately after the sight has
been taken, it being necessary only to add or subtract the altitude. (See art. 323.)
It is assumed that the noon longitude will be sufficiently accurately known in
advance to enable the navigator to correct the declination; also the approximate
meridian altitude to correct the parallax and refraction ; if the latter is not known,
it may readily be found from the declination and approximate latitude.
(Generally speaking,
Lat. = Zenith distance + Dec . ,
= 90 -True alt. + Dec.,
= 90 - (Obs. alt. + Corr.) + Dec.,
= (90 + Dec. - Corr.) - Obs. alt.,
LATITUDE. 129
in which the quantity (90 -f Dec. Coir.) may be termed a Constant for the meridian
altitude of the day, as it remains the same regardless of what the observed altitude
may prove to be. The constant having been worked up before the observation is
made, the latitude will be known as soon as the observed altitude is applied.
To avoid the confusion that might arise from the necessity of combining the
terms algebraically according to their different names, it may be convenient to divide
the problem into four cases and lay down rules for the arithmetical combination of
the terms, disregarding their respective names as follows :
Case I. Lat. and Dec. same name, Lat. greater, -f 90 + Dec. Coir. Obs. alt.
Case II. Lat. and Dec. same name, Dec. greater, 90 + Dec. -fCorr. + Obs. alt.
Case III. Lat. and Dec. opposite names, + 90 Dec. Corr. Obs. alt.
Case IV. Lat. and Dec. same name, lower transit, +90 Dec. + Corr. + Obs. alt.
The correctness of such an arrangement will become readily apparent from an
inspection of figure 50. The assumption has been made that tne correction to the
observed altitude is positive ; when this is not true the sign of the correction must
be reversed.
As examples of this method, the first, second, third, and fifth of the examples
previously given illustrating the meridian altitude will be worked, using the constant;
the details by which Corr. and Dec. are obtained are omitted, being the same as in
the originals.
IST EXAMPLE. 2D EXAMPLE. 3o EXAMPLE. STH EXAMPLE.
Case I. Case II. Case III. Case IV.
+ 90 00 00" -90 00 00" +90 00 00" +90 00 00"
Dec., + 23 27 06 Dec., + 9 15 00 Dec., -18 51 24 Dec., -23 15 08
Corr., - 13 21 Corr., + 9 00 Corr., - 12 02 Corr., + 5 11
Constant, + 113 13 45 Constant, -80 36 00 Constant, +70 56 34 Constant, +66 50 03
Obs. alt., - 40 04 00 Obs. alt., +81 15 30 Obs. alt., -30 13 10 Obs. alt., + 8 16 10
Lat., 73 09 45 (N.) Lat., 39 30 (N.) Lat., 40 43 24 (S.) Lat., 75 06 13 (N.)
BY BEDUCTION TO THE MERIDIAN.
326. Should the meridian observation be lost, owing to clouds or for other
reason, altitudes may be taken near the meridian and the times noted by a watch
compared with the chronometer, from which, knowing the longitude, the hour angle
may be deduced.
If the observations are within 26 m from the meridian, before or after, the correc
tion to be applied to the observed altitude to reduce it to the meridian altitude may
be found by inspection of Tables 26 and 27. Table 26 contains the variation of the
altitude for one minute from the meridian, expressed in seconds and tenths of a
second. Table 27 contains the product obtained by multiplying the square of the
minutes and seconds by the change of altitude in one minute.
Let a = change of altitude (in seconds of arc) in one minute from the meridian:
H = meridian altitude;
Ji = corrected altitude at observation; and
t = interval from meridian passage.
The value of the reduction to the meridian altitude of each altitude is found by
the formula:
a being found in Table 26, and at 2 in Table 27; hence the following rule:
Find the hour angle of the body in minutes and seconds of time. Take from
Table 26 the value of a corresponding to the declination and the latitude. Take
from Table 27 the value of at 2 corresponding to the a thus found and to the interval,
in minutes and seconds, from meridian passage. This quantity will represent the
amount necessary to reduce the corrected altitude at the time of observation to the
corrected altitude at the meridian passage; it is always additive when the body is
near upper transit, and always to be subtracted when near lower transit.
If the mean of a number of sights is to be taken, determine each reduction sepa
rately, take the mean of all the reductions, and apply it to the mean of the altitudes;
61828 16 - 9
130 LATITUDE.
it is incorrect, in such a case, to take the mean of the times and work the sight with
this single value of t. The differences of altitude being small, the parallax and
refraction will .be sensibly the same for all, and one computation of the correction to
the observed altitude will suffice.
Knowing the meridian altitude, the latitude is to be found as previously explained.
327. When several sights are taken, the most expeditious method of calculating
will be to find first the watch time of transit, and thence obtain the hour angle of each
observation by comparing the watch time of observation. The watch time of transit
may be found as already explained (art. 323) for computing that quantity as a guide
in taking the meridian altitude, but the hour angle thus obtained is subject to a
correction. The difference between watch time of transit and watch time of observa
tion gives the watch time that is, the mean time elapsing between transit and
observation. A fixed star covers in that time an angle corresponding to the sidereal
and not to the mean time interval, and a reduction should be made accordingly to
give its true hour angle at the instant of observation. A planet s hour angle should
be corrected in the same way (for we may disregard its very small change in right
ascension) . The correction may be entirely neglected in the case of the sun, as the
diiference between mean and apparent time intervals is immaterial. The reduction
of the hour angle in the case of the moon becomes rather cumbersome, so much so
that it is better to find the hour angle of this body by the more usual method of
converting watch time to G. M. T., and thence to L. S. T., and finding the difference
between the latter and the R. A. ; an additional reason for this is that the G. M. T.
of observation must be known exactly, with the moon, for the correction of the
declination (art. 330).
328. Table 26 includes values of the latitude up to 60, and those of the declina
tion up to 63, thus taking in all frequented waters of the globe and all heavenly
bodies that the navigator is likely to employ. No values 01 a are given when the
altitudes are above 86 or below 6, as the method of reduction to the meridian is
not accurate when the body transits very near the zenith, and the altitudes themselves
are questionable when very low. In case it is desired to find the change of altitude
in one minute from noon for conditions not given in the tables, it may be computed
by the formula:
_ l"-9635 cos L cos d
sin (L d)
In working sights by this method where great accuracy is required, as in deter
mining latitudes on shore for surveying purposes, it is well to compute the a rather
than to take it from the table, as one is thus enabled to employ the value as found to |
the second decimal place.
Due regard must be paid to the names of the declination and latitude in working
this formula; if they are of opposite names, the declination is negative, and L and a
should be added together to obtain L d.
329. Table 27 contains values of at 2 up to the limits within which the method ,
is considered to apply with a fair degree of accuracy. It must not be understood
that the plan of reduction to the meridian is not available for wider limits, but it
would seem preferable to employ the <j> <$>" formula, described hereafter, when the
hour angle falls beyond that for which the table is computed. On the other hand,
the reduction is not exact in all cases covered by the table; while sufficiently so for
sea navigation, the limits given are far too wide for the precise determinations
required in surveying, where the aim should be to observe bodies under such conditions
that the total reduction at 2 shall not exceed 1 .
330. It should be kept clearly in mind when employing the method of reduction
to the meridian that the resulting latitude is that of the ship at the instant of observa
tion, and to bring it up to noon the run must be applied. The declination should
properly be corrected for the instant of observation; with the sun or a planet, it is
sufficiently accurate to use the declination at meridian passage, unless the^ interval
from the meridian be quite large; but the moon s declination changes so rapidly that
the exact time of observation must be used in its correction when working with
this body.
LATITUDE. 131
EXAMPLE: In latitude 47 S., having previously worked up the constant for meridian altitude,
78 42 10", observed altitude of sun near meridian, 31 ll/ 50"; Dec. 11 N.; watch time, ll h 40 21",
watch fast of L. A. T., 7 s . Find the latitude.
Watch time, ll h 40 21- Obs. alt., 31 IV 50" a (Tab. 26), 1".6
Watch fast, 07 at*, + 10 24
Her. alt,, 31 22 14 (1".0=6 / 30 /
Constant, 78 42 10 ^ (Tab 2?) I . 6= 3 54
Lat., 47 19 56 S. [l .6=10 24
EXAMPLE: At sea, July 12, 1916, in Lat. 50 N., Long. 40 W., observed circum-meridian altitude of
the sun s lower limb, 61 48 30", the time by a chronometer regulated to Greenwich mean time being
2 n 4im 395. c kro. corr>j _2m 30 I. C., 3 0"; height of the eye, 15 feet. Find the latitude.
Chro t 2 h 41 m 39" Q 61 48 30" Dec. 2 h , 21 58 . 9 N. Eq.t.2 h ., 5 m 24M
C. C., - 2 30 Corr., + 8 31
H. D., - V.4 H. D., + 0".3
G. M. T., 2 39 09 Ji, 61 57 01 G. M. T., 0*. 65 G. M. T., 0*. 65
Eq. t., -^ ^ (Tab. 46),+ IV 31" Corr., - O 7 . 26 Corr., + OM95
G. A. T., 2 33 44.7 I.C., - 3 00
Long -2 40 00.0 Dec., 21 58 38"N. Eq. t., 5 m 24. 3
Corr., + 8 31" (Subtract from mean
L. A. T., 11 53 44.7 time.)
t, 6 15.3
ft, 61 57 01" a (Tab. 26), 2". 5
a 2 ,+ 1 38
* ro// t) -t/ no//
H, 61 58 39 ?~ 90
gp(Tab.27),j 5==
2, 28 01 21 N. o *_i QG
J, 21 58 38 N.
L, 49 59 59 N.
EXAMPLE: May 31, 1916, in Lat, 30 15 N., Long. 5 h 25 m 42" W., about 9 p. m., observed with a
sextant and artificial horizon a series of altitudes of Spica; mean observed double altitude 98 06 34";
noted times as enumerated below by a watch compared with a chronometer which was 2 m 33 s fast of
G. M. T.; C-W, 5 h 29 m 40 s ; I. C.,-3 00". Find the latitude.
p .t- /T o rr\
transit) 13 h 20 m 48 s . 9 Mean 2 alt, *, 98 06 X 34" R. A. *, 13 h 20 48". 9
Long + 5 25 42 I. C., - 3 00 _,
T Dec., 10 43 X 42" S.
GST 18 46 30.9 2)98 03 34 ___
R \ M S. Gr. 0", 4 34 36 . 1 a (Tab. 26), 2". 5
49 01 47
Sid. int. from O 11 , 14 11*54.8 ref., - 50
Red. (Tab. 8), - 2 19 . 7
h, 49 00 57
G. M. T., 14 09 35.1
C. C. (sign reversed), + 2 33
Chro. time transit, 14 12 08 . 1
C-W, - 5 29 40
Watch time transit, 8 42 28
Intervals from transit, at 2 (Tab. 27).
Watch times. Meantime. Sid. time. 2.0 0.5 2.5 h, 49 OO 7 57" ;
8 ti 33 m 05 s .O - 9 m 23 s . - 9 m 24 2 56" (X 44" 3 7 40" at 2 , + 1 40
35 06.5 7 21.5 7 23 1 49 27 2 16
37 54.0 4 34.0 4 35 42 10 52 H, 49 02 37
40 37.0 1 51.0 1 51 07 02 09
42 54 . 5 -f 26 . 5 + 27 00 00 00 z, 40 57 23 N.
45 32.5 3 04.5 3 05 19 04 23 d, 10 43 42 S.
47 33.0 5 05.0 5 06 52 13 1 05
49 20.0 6 52.0 6 53 1 35 23 1 58 L, 30 13 41 N.
52 59.5 10 31.5 10 33 3 42 55 4 37
9)15 00
1 40
132
LATITUDE.
EXAMPLE: August 6, 1916, Lat. 59 S., Long. 175 27 E., during evening twilight, observed an
altitude of Achernar, near lower transit, 26 52 ; watch time, 4 h 31 m 12 s ; C-W, O h 18 m 07 - chro fast of
G. M. T., 12 m 42 s ; I. C., +1 20"; height of eye, 24 ft. Find hour angle by both methods; thence the
latitude.
R. A. # + 12 h \
L. S. T. lower trans./
Long.,
G. S. T.,
R. A. M. S. Gr. 5 d O h , -
Sid. int.,
Red. (Tab. 8),
G. M. T.,
C. C. (sign reversed), +
Chro. time,
C-W,
Watch time transit,
Watch time oba.,
. /Meantime,
1 \Sid. time,
Obs. alt. #, 26 52 00"
Corr., 5 23
h,
13 h
11
34 m
41
38.4
48
1
8
52
54
50.4
48.9
16
58
2
01.5
46.8
16
55
12
14.7
42
5
07
18
56.7
07
4
4
49
31
49.7
12
18
18
37.7
40.8
Watch time,
C-W,
Chro. t.,
C. C.,
G. M. T. 5 d
R. A. M. S. Gr. 5 d O h , +
Red. (Tab. 9),
G. S. T.,
Long.,
L. S. T.,
R. A. # -f 12 h
4 h
31*
1 12 s
+ o
18
07
4
49
19
12
42
16
36
37
+ 8
54
48.9
+
2
43.7
1
34
09.6
+ 11
41
48
13
15
57.6
13
34
38.4
(Tab. 46), -6 43"
I.C., +1 20
H,
P,
26 46 37"
3 29
26 43 08
32 20 48
59 03 56 S.
Corr.,
5 23
R. A. #,
Dec.,
P,
a (Tab. 26),
at 2 (Tab. 27),
18 40.8
l h 34 m 38. 8 4
57 39 12" S.
32 20 48
0".6
3 29"
331 . Advantages are gained in working out meridian altitudes and reductions to
ike meridian, in finding the constant for a meridian altitude or a reduction to the
meridian, and in predicting the approximate altitude of a body to be observed on
or near the meridian, by projecting, in a quickly and roughly drawn diagram on the
plane of the meridian of the observer, the known data entering into the problem.
The diagram or figure will show at once how to combine the data to find the required
result, and its use tends greatly to accuracy. It is
only necessary to know the meaning of the terms
already defined and to remember the single principle
that the latitude of a place is equal to the declination
of its zenith.
In every case draw a circle (a rough approxima
tion will do) to represent the plane of the meridianj as
in figure 51. The center O is the position of the ob
server. Draw a horizontal line through O, marking
its intersection with the circumference on the right-
hand side S, and on the left-hand side N. Erect a
perpendicular to this line at O, and mark its inter
section with the circumference Z. The line NS is
the horizon; Z is the zenith. The arc ZS is that por
tion of the meridian between the zenith and the south
point of the horizon; the arc ZN is that portion of the
meridian between the zenith and the north point of the horizon. If the meridian
altitude of a body is known (i. e., its altitude above the horizon on the meridian),
and if it is known whether it bears to the southward or to the northward, its posi-
FlO. 51.
LATITUDE. 133
tion can be projected at once on the figure. Having the position of the heavenly
body on the meridian and knowing the declination of the body, it is evident where
to draw in the projection of the equator. Having the projection of the equator,
the angular distance between the equator and the
zenith (i. e., the declination of the zenith) is the
latitude.
Thus in figure 52, supposing the meridian alti
tude of any heavenly body, M, nas been observed,
and that at the time of observation it was bearing
south; also that the declination, d, of the body was
south. It is known that the true altitude, h, =
observed altitude altitude coir. Since the body
bears south, if the true altitude is h, the position
of the body, M, can be located by laying off the
arc SM=ft, or bv drawing OM so that tne angle
BOM = ft. This gives the position of the heavenly
body on the meridian. Since this body is south of _
the equator by the amount of the declination, the FIG. 52.
position of the equator may be drawn by laying off
the angle MOQ = a. OQ is the projection of the equator, and the arc ZQ (or the
angle ZOQ), being the declination of the zenith, is equal to the latitude. The for
mula for finding the latitude may be written by inspection of the figure:
L = 90-(ft + <Z) = 90-A-(Z. (1)
Since ^=obs. alt.corr.,
L=90-obs. alt.corr.-d. (2)
By a similar process formulae may be written for determining the approximate
altitude of the heavenly body when on the meridian and for getting a noon constant.
The former is necessary to get the altitude correction before taking the sight ; the
latter, so that the latitude may be obtained as soon as the altitude is read from the
sextant. In these cases the D. R. latitude and longitude, which have to be worked
out in advance for noon, are used. The longitude is used to get the correction to be
applied to the equation of time to get the G. M. T. of local apparent noon in order to
get the correct declination at Local Apparent Noon at the noon position. Knowing
the approximate latitude and the declination, they are projected on the figure in this
way. If the latitude is north, the zenith is to the northward of the equator by
the amount of the latitude, and to get the position of the equator lay off the angle
ZOQ = Lat. If the latitude were south, the equator would of course be on the north
side of the zenith by the amount of the latitude, and OQ would be on the north side of
the circle. Having the position of the equator, draw in the position of the heavenly
body by laying it off to the north side or to the south side of the equator according
to the amount and direction of its declination. The angle between the horizon and
the heavenly body will be the altitude of the body. This is the usual method of
plotting, and all that has to be done is to lay the angles off on the proper sides,
marking them appropriately, and then write down the formulae. Suppose it is
required to find the approximate noon altitude. An inspection of the figure shows
that
approx. 7i = 90 - (L + d) where L is the D. R. Lat. (3)
Suppose it is required to find the constant (K) for a meridian altitude. It is
seen from the figure that
= K-obs. alt.
or
K = 90corr.-d. (4)
In the same way any combination may be plotted, and the correct formulae may
be written out at once. Suppose on a certain day it is found that at noon the
position will be approximately Lat. 10 S., Long. 30 15 W., and that the declination
of the sun at noon, corrected for G. M. T. of local apparent noon at the noon position,
134
LATITUDE.
is 20 30 S., and it is desired to find the approximate noon altitude and obtain the
constant, K. Draw the circle representing the plane of the meridian (see fig. 53),
draw NS representing the horizon, and OZ representing the line to the zenith. Since
the approximate latitude is 10 S, the equator must be 10 north of the zenith, and
OQ is drawn to the north of Z so that the angle ZOQ = 10. OQ is then the pro
jection of the equator^ JThe body being 20 30 south
M f
the equator, lay off OM so that the angle QOM =
20 30 . SOM will be the approximate altitude, and
the formula for it is
approx. 7i = 90 + L - d
it is also seen that
SL
(5)
alt.
or
If, instead of the formulae for a meridian altitude,
the formulsB for a reduction to the meridian are re-
no. 53. quired, ^there is no change in the figure or the method.
The altitude observed before or after noon is corrected
to make it the noon altitude by the formula Ji = 1\> + at 2 , where h is the noon alti
tude, h the altitude observed t minutes before or after noon, and a the rate of
change of altitude near noon. So that in the case shown in figure 53
or
The formula for the approximate value of h, as shown in (5), is used for getting
the altitude correction in this case, as the slight difference in altitude makes no
change in the correction.
The formula for latitude, given in equation (6), is the formula for the latitude at
noon at the point where the observation was taken. But a ship steaming on a
course does not remain at that point, and what is desired is the correct latitude of
the ship s position at noon. If L represents the latitude of the place where the
observation was taken, and L the latitude of the place where the ship is at noon,
then L = L JL, where JLis the change in latitude from the time of observation
until noon. This is taken from the Traverse Tables. But from equation (6) it is
seen that L = obs. alt. corr. + at 2 + d - 90
or
. .L=L JL=obs. alt
= K + obs. alt.
K=
BY A SINGLE ALTITUDE AT A GIVEN TIME.
332. This observation should be limited to conditions where the body is within
three hours of meridian passage and where it is not more than 45 from the meridian
in azimuth; also where the declination is at least 3. On ^the prime vertical the
solution by this method is inexact, and when the hour angle is 6 h , or the declination
0, it is impracticable.
The problem is: Given the hour angle, declination, and altitude; to find the
latitude. The solution is accomplished by letting fall, in the usual astronomical
triangle, a perpendicular from the body to the meridian, and considering separately
the distances on the meridian, from the pole and zenith, respectively, to the j)oint
of intersection of the perpendicular; the sum or difference of these distances is the
co-latitude.
LATITUDE. 135
Following the usual designation of terms and introducing the auxiliaries <j>
and <", the formulae are as follows:
tan (f>" = tan d sec t;
cos </> =sin h sin <j>" cosec d;
lj == <z> -j- o .
The terms </> and (f)" will have different directions of application according to
the position of the body relative to the observer. From a knowledge of the
approximate latitude, the method of combining them will usually be apparent; it is
better, however, to have a definite plan for so doing, and this may be based upon the
following rule :
Mark <j>" north or south, according to the name of the declination; mark <
north or south, according to the name of the zenith distance, it being north if the
body bears south and east or south and west, and south if the body bears north and
east or north and west. Then combine cf>" and < according to their names; the
result will be the latitude, except in the case of bodies near lower transit, when
180 <f>" must be substituted for $" to obtain the latitude.^
It may readily be noted that if we substitute $" for declination and <j> for zenith
distance, the problem takes the form of a meridian altitude; indeed, the method
resolves itself into the finding of the zenith distance and declination of that point on
the meridian at which the latter is intersected by a perpendicular let fall from the
observed body.
The time should be noted at the instant of observation, frotn which is found the
local time, and thence the hour angle of the celestial object.
If the sun is observed, the hour angle is the L. A. T. in the case of a p. m. sight,
or 12 h L. A. T. for an a. m. sight. If any other body, the hour angle may be found
as hitherto explained.
EXAMPLE: June 7, 1916, in Lat. 30 25 N., Long. 81 25 30" W., by account; chro. time, 6 h 22 m 52 ;
obs. Q 75 13 , bearing south and west; I. C., 3 00" , height of the eye, 25 feet; chro. corr. -2 m 36 s .
Find the latitude.
Chro. t, 6h 22m 52 Obs.alt.Q, 75 13 00" Eq. t., 6^, 1 20-.4 Dec., &&gt;, 22 46 .6 N.
C. C., 2 36 Corr., -f 7 39 Coir., .2 Corr., + .07
G.M.T., 6 20 16 A, 75 20 39 Eq.t., 1 20.2 Dec., 22 46 40" N.
(Tab. 46). + 10 39" H. D., - 0*.5 H. D., + .2
G.A.T., 6 21 36 I. C., - 3 00 G. M. T., Qh.3 G. M. T., Qh.33
Long., - 5 25 42
Corr., + 7 39" Corr., - O.15 Corr., .066
TAT/ / Oh 55"* 54 "VY". (Add to mean time.)
L.A.T.=f, \ ir & 30"
t, 13 58 30" sec . 01305
d, 22 46 40 tan 9.62315 cosec .41211
75 20 39 sin 9.98563
23 23 55 N. tan 9.63620 sin 9.59893
7 05 00 X. cos 9.99667
Lat., 30 28 55 X.
EXAMPLE: October 10, 1916, p. m., in Lat. 6 20 S. by account, Long. 30 21 30" W.; chro. time,
12 h 45 m 10; observed altitude of moon s upper limb, 70 15 30", bearing north and east; I. C., 3 00"]
height of eye, 26 feet; chro. fast of G. M. T., l m 37 8 .5. Required the latitude.
Chro.t., 12h 45m iQe Obs.alt. d, 70 15 30" R. A. C (12h), Oh 42m 16- Dec.(12h), 9 52 .9 N.
C. C., - 1 37.5 Corr., - 4 27 Corr., -f 1 32 Corr., + 10.1
G.M.T., 12 43 32.5 h, 70 11 03 R. A., Oh 43" 48 Dec., 10 03 N.
Red.(Tab.9),+ 2 05.4 (Tab. 49), - 1 27" H. D., + 128-.5 H. D., + 14 .05
I.C., - 3 00" G. M. T., Oh.?2 G.M.T., Qh.72
G.S.T., 2 00 39.3
R.A., - 43 48.0 COTT ., - 4 27" Corr., + 92".5 Corr., + lO .ll
H.A.fromGr., 1 16 51.3W.
Long., 2 01 26 .0 W.
i??#i R Hor - Par " 58MS "
136
LATITUDE.
t. 11 08 40 //
d, 10 03 00
h, 70 11 03
<", 10 14 21 N.
< , 16 36 00 S.
Lat. 6 21 39 S.
sec
tan
. 00827
9.24853
cosec .75819
tan 9.25680
sn
sin
cos
9.97349
9.24983
9. 98151
EXAMPLE: August 6, 1916, p. m., in Lat. 52 W S. by D. R., Long. 146 32 E., observed altitude of
Achernar, near lower transit, 24 OK 20" bearing south and east; watch time, 6 h 48 m 22 s ; C-W, 2 h 13 m
33 ; chro. corr. on G. M. T., + l m 57 s ; height of eye, 18 feet; I. C. +1 / 00". Find the latitude.
Watch time,
C-W,
Chro. t.,
C.C.,
6 h 48 m 22-
+ 2 13 33
9 01 55
+ 1 57
Obs. alt.*,24 OF 20"
Corr., - 5 19
G. M. T. 5 d , 21 03 52
R.A. M. S., + 8 54 48.9
Red. (Tab. 9), + 3 27.6
(Tab. 46),
I. C.,
Corr.,
23 56 01
-
- 6 19"
+ 1 00
R. A.
Dec.,
:, l h 34 m 38 S .4
57 39 12" S.
- 5 19"
G.
S.
T.,
6
02
08.
5
R.
A.
*,
1
34
38.
4
H.
A.
from Gr.,
4
27
30.
1W.
Long.
9
46
08
E.
H.
A.
p
14
13
38
W.
9
46
22
E.
i
2 h
33
13"
24
>38 8
30 /
/
i
33
57
24
39
30
12
h,
23
56
01
180 -V , 117
51
52 S.
,
64
52
49 N.
Lat.
t
52
59
03 S.
sec. . 07843
tan. . 19838
tan. .27681
cosec.
sin.
sin.
cos.
.07323
9.60818
9. 94648
9. 62789
If the sidereal time is
BY THE POLE STAB.
333. This method, confined to northern latitudes, is available when the star
Polaris and the horizon are distinctly visible, the time of the observation being noted
at the moment the altitude is measured.
Reduce the observed altitude of Polaris to the true altitude.
.Reduce the recorded time of observation to the local sidereal time.
less than lh 29.2m, subtract it from lh 29.2m;
between lh 29.2m and 13h 29.2m, subtract lh 29.2m
from it ;
greater than 13h 29.2m, subtract it from 25h 29.2m;
and the remainder is the hour-angle of Polaris.
With this hour-angle take out the correction from Table I of the Nautical
Almanac, and add it to or subtract it from the true altitude, according to its sign.
The result is the approximate latitude of the place.
EXAMPLE: 1916, August 5, at 10 11 40 m 30 s p. m. local mean solar time, in longitude 59 west of Green
wich, suppose the true altitude of Polaris to be 33 20 X 0", required the latitude of the place.
Local astronomical mean time 10 h 40 m 30
Reduction from Table 9 for 10 h 40 m 30 s + 01 45
Greenwich sidereal time of mean noon, August 5 8 54 49
Reduction from Table 9 for longitude (=3 b 56 m west, or plus) + 00 39
Sum (having regard to signs) is equal to local sidereal time 19 37 43
Subtract sidereal time..
25 h 29 m 12 s
19 37 43
Remainder is equal to hour angle of Polaris
5 51 29
LATITUDE.
137
True altitude +33 20 00"
Correction from Table I of the Nautical Almanac 1 51
Approximate latitude of the place +33 18 09
Observations of Polaris for latitude should be made when practicable near the
times of upper or of lower culminations (hour angle O h or 12 h ). However, at sea,
if made near elongation (hour angle 6 h or 18 h ), the hour angle, and hence the local
time, should be known within one minute.
334. The latitude may be approximately found from an altitude of Polaris by
computation from the formula:
L = h p cos t ,
in which,
h = true altitude, deduced from the observed altitude ;
p = polar distance = 90 d, the apparent decimation being taken from the
Nautical Almanac for the time of observation.
t = star s hour angle.
Reduce the recorded time of observation to the local sidereal time.
Take out, from the Nautical Almanac, the apparent right ascension of Polaris
for the time of observation.
Subtract the apparent right ascension from the local sidereal time, and the
remainder will be tne hour angle.
To the log cosine of the hour angle add the logarithm of the polar distance in
minutes; the number corresponding to the resulting logarithm will be a correction
in minutes to be subtracted from the star s true altitude to find the latitude when the
hour angle is less than 6 h or more than 18 h , and to be added to the star s true altitude
to find the latitude when the hour angle is more than 6 h and less than 18 h .
EXAMPLE: June 11, 1916, from an observed altitude of Polaris, the true altitude was found to be
29 5 55". The time noted by a Greenwich chronometer was 13 h 41 m 26 s ; chro. corr.-2 m 22 ; Long.
5 h 25m 42 s W.
Chro. time,
C.C.,
G. M. T., ll d ,
R. A. M. S.,
Red. (Tab. 9),
13 h
41"
2
1 26
22
+
+
13
5
39
17
2
04
58.2
14.5
p cos
Lat.,
29 05
t,+ 1 08
55"
36
30 14 31 N.
R. A.
Dec.,
l h 29 m 19
88 51
G. S. T., 18 59 17
R. A. #, - 1 29 19
H. A. fromGr.,
Long.,
H. A.,
17 29 58 W.
5 25 42 W.
12 04 16 W.
/ ll h 55 m 44 s E.
\178 56 00"
P,
p, 68 . 6
t, 178 56
.
pcos f,-
68 .
08 /
log 1. 83632
cos(-) 9.99992
-) 1.83624
If the computation is extended according to the following formula, inserting the
value of p in seconds of arc :
p* sin 1" sin 2 1 tan h,
cos
the resulting latitude is subject to no greater error than 1" ; but if p cos t is the only
correction applied to the altitude of Polaris, as in the above example, the resulting
latitude, while subject to little error when Polaris is observed near the meridian, wifl
have an error, when t = 6 hours, increasing with the altitude and amounting to 1
when ft = 54 and to 3 when ft = 68 30 .
DETERMINATION ON SHORE.
335. In finding the latitude on shore all the methods are available that have
been heretofore explained for employment in finding the latitude at sea, provided
only that an artificial horizon (art. 256) be supplied to take the place of the natural
horizon of the sea in obtaining a measurement, by the sextant, or the altitude of the
celestial body. In addition, other methods may be conveniently employed, involving
138 LATITUDE.
the use of a theodolite or an altazimuth instrument, which the observer at sea is
precluded from using because the employment of such instruments requires a steady
platform.
If the observation is to be made with a theodolite or altazimuth > the instrument
must first be placed level so that the line of collimation of the telescope revolves in
the plane of the true meridian. This may be accomplished by means of laying off a
true meridian from the true bearing of a terrestrial object from the instrument, as
determined by the observation described in articles 360 and 361.
The altitude of the celestial body is then measured by bringing the horizontal
cross wire of the telescope on the body at the instant the body transits the meridian
or crosses the vertical cross wire of the telescope, and then reading the vertical
circle.
The latitude is then deduced from the formula, ~L = d + z, after applying the proper
corrections for index error, parallax, and refraction. The correction for index error
is obtained by bringing the telescope to a horizontal position, as indicated by the
level tube attached to the telescope, and taking the corresponding reading of the
vertical circle immediately before and after each observation.
By observing the altitude of each of two stars with approximately the same
zenith distance, one north of the zenith and one south of the zenith, a mean value
for latitude resulting from the two observations may be obtained which is not
affected by the error in estimating the absolute value of the astronomical refraction,
but simply by the error in estimating a very small difference of refraction of two
stars at nearly the same altitude.
This method of determining the latitude of a station is known as the Horrebow-
Talcott method, and consists of the measurement of the small differences of zenith
distance of two stars which transit at about the same time on opposite sides of the
zenith. The effect of this procedure is the attainment of greater precision due to
the increased accuracy of a differential measurement over the corresponding absolute
measurement, the elimination of the use of a graduated circle in the measurement,
and the fact that the computed result is not affected by the error in estimating the
absolute value of the astronomical refraction, but simply by the error in estimating
a very small difference of refraction of two stars at nearly the same altitude.
After measuring the difference of meridional zenith distances of two stars which
transit at about the same time on opposite sides of the zenith and with nearly the
same zenith distances, the latitude may be deduced from the following formula:
Let d = decimation of star south of zenith.
d = declination of star north of zenith.
2 = zenith distance of star south of zenith.
z = zenith distance of star north of zenith.
Then L = d + z
that is, the latitude is equal to one-half the sum of the declinations plus one-half the
difference of zenith distances. The form of instrument used in measuring the differ
ences of zenith distances is known as a zenith telescope, and consists of a telescope
mounted on a horizontal axis supported by an upright or uprights in such a manner
that it can be revolved about a vertical axis. A vertical circle is attached to the
telescope for use in setting the telescope at the proper inclination with the horizontal i
to bring a particular star into the field of the telescope. A level tube is also attached
to the telescope for use in bringing the telescope to the same inclination when observ
ing on each of a pair of stars. The eyepiece of the telescope is fitted with a micro
meter screw which operates a movable horizontal cross wire with which the bisections
of the image of the observed body are made.
The process of observing for difference of zenith distances is as follows: If the
first star of the pair of stars to be observed has a] soll th zenith distance the telescope
is revolved about its vertical axis until it pointsj sou t n i n the plane of the meridian.
LATITUDE. 139
The approximate mean zenith distance of the two stars is then set off on the vertical
circle, and the level bubble brought to the center of the tube. When the star appears
in the field of the telescope the horizontal cross wire is brought to bisect the star
and such bisection retained until the star crosses the vertical cross wire of the tele
scope. The micrometer head is then read. The telescope is then revolved through
180 about its vertical axis and brought to the same inclination with the horizontal
by moving the telescope itself about its horizontal axis^ until the level bubble is at
the center of the tube. In like manner the second star is bisected by the horizontal
cross wire and the micrometer head again read. The difference between the two
micrometer readings gives the difference of zenith distances of the two stars in terms
of divisions of the micrometer, which when multiplied by the known angular value
of one division of the micrometer gives the angular difference of the zenith distances
of the two stars.
CHAPTER XIII.
LONGITUDE.
336. The longitude of a position on the earth s surface is measured by the arc
of the equator intercepted between the prime meridian and the meridian passing
through the place, or by the angle at the pole between those two meridians.
Meridians are great circles of the terrestrial sphere passing through the poles.
The prime meridian is that one assumed as the origin, passing through the
location of some principal observatory, such as Greenwich, Paris, or Washington. That
of Greenwich is the prime meridian not only for English and American navigators, but
for those of many other nations.
Secondary meridians are those connected with the primary meridian, directly
or indirectly, by exchange of telegraphic time signals.
Tertiary meridians are those connected with secondaries by carrying time in the
most careful manner with all possible corrections.
Longitude is found by taking the difference between the hour angle of a celestial
body from the prime meridian and its hour angle, at the same instant, from the local
meridian. In determinations ashore the hour angle from the prime meridian may
be found either from chronometers or from telegraphic signals; the local hour angle
may be found by transit instrument or by sextant. In determinations at sea the
chronometer and sextant give the only means available.
DETERMINATION ON SHORE.
337. TELEGRAPHIC DETERMINATION OF SECONDARY MERIDIANS. In order to
locate with accuracy the positions of prominent points on the coasts, it is necessary
to refer them, by chronometric measurements, to secondary meridians of longitude
which have been determined with the utmost degree of care.
Before the establishment of telegraphic cables, this was attempted principally
through the observation of moon culminations, which seemed always to carry with
them unavoidable errors, or by transporting to and fro a large number of chronometers
between the principal observatory and the position to be located; and in this method
it can be conceived that errors would be involved, no matter how thorough the
theoretical compensation for error of the instruments.
By the aid of telegraph and radio, differences of longitude are determined with
great accuracy, and an ever-increasing number of secondary meridional positions are
thus established over the world; these afford the necessary bases in carrying on the
surveys to map correctly the various coast lines, and render possible the publication
of reliable and accurate navigators charts.
338. To determine telegraphically the difference of longitude between two points,
a small observatory containing a transit instrument, ^chronograph, break-circuit
sidereal chronometer, and a set of telegraph instruments is established at each of the
two points, and, being connected by a temporary wire with the cable or land line at
each place, the two observatories are placed in telegraphic communication with each
other.
By means of transit observations of stars, the error of the chronometer at each
place on its own local sidereal time is well determined, and the chronometers are
then accurately compared by signals sent first one way and then the other, the times
of sending and receiving being very exactly noted at the respective stations. The
error of each chronometer on local sidereal time being applied to its reading, the
difference between the local times of the two places may be found, and consequently
the difference of longitude. The time of transmission over the telegraph line is
eliminated by sending signals both ways. By the employment of chronometers
14O
LONGITUDE. 141
keeping sidereal time, the computation is simplified, though mean-time chronometers
may be used.
339. ESTABLISHMENT OF TERTIARY MERIDIANS. Let it be supposed that the
meridional distance between A and B is to be measured, of which A is a secondary
meridional position accurately determined, and B a tertiary meridional position to
be determined.
If possible, two sets of observations should be taken at A to ascertain the errors
and rates of the chronometers. The run is then made to B, and observations made
to determine local time, and hence the difference of longitude; and on the same spot
altitudes of the sun, or of a number of pairs of stars, or both, should be taken to
determine the latitude.
Now, if chronometer rates could be relied on to be uniform, this measurement
would suffice, but since variations may always arise, the run back to A should be
made, or to another secondary meridional position, C, and new rates there obtained.
Finally, the errors of the chronometers on the day when the observations were made
at the tertiary position should be corrected for the loss or gain in rate, and for the
difference of the errors as thus determined.
When opportunity does not permit obtaining a rate at the secondary meridional
station or stations, both before and after the observations at B, the navigator may
obtain the .errors only, and assume that the rate has been uniform between those
errors.
A modification of the foregoing method which may sometimes prove convenient
is to make the first and third sets of observations at the position of the tertiary
meridian, and the intermediate one at the secondary meridian; in this case the error
will be obtained at the secondary station and the rate at the tertiary.
EXAMPLE: A vessel at a station A, of known longitude, obtained chronometer errors as follows:
May 27, noon, chro. slow, 7 m 18 . 9,
June 3, noon, chro. slow, 7 12 . 7;
then proceeding to a station B a series of observations for longitude was taken on June 17; after which,
returning to A, the following errors were obtained:
July 3, noon, chro. slow, 7 m 00*. 7,
July 10, noon, chro. slow, 6 59 . 8.
Required the correct error on June 17.
May 27, -7 m 18*. 9 July 3, -7 m OO 4 . 7
JuneS, -7 12.7 July 10, -6 59.8
Change, -f- 6.2 Change, +
Daily rate, + s . 89 Daily rate, +
Therefore, assuming that these rates were correct at the middle of the periods for which they were
determined, we have,
May 30, Midnight, Rate, +0 . 89
July 6, Midnight, Rate, +0 . 13
Change of rate, 37 days, . 76
Daily change of rate, s . 021
Change of rate for 3 days, -O f .07; rate June 3, noon, +0.89-0 a .07=+0 i . 82
Change of rate for \1\ days, -0 .37; rate June 17, noon, +0 .89-0 .37= +0 . 52
Mean daily rate, June 3 to 17, +0 . 67
Total change of error, June 3 to 17, +0 m 09*. 38
Error, June 3, -7 12 . 7
Error, June 17, -7 03 . 3
34:0. SINGLE ALTITUDES. The determination of longitudes on shore by single
altitudes of a celestial body is identical in principle with the determination at sea
by that method, which will be explained hereafter (art. 341). It may be remarked,
however, that by taking observations on opposite sides of the meridian, at altitudes
as nearly equal as posssible, a means is afforded, which is not available at sea, of elimi
nating certain constant errors of observation.
142
LONGITUDE.
DETERMINATION AT SEA.
341. THE TIME SIGHT. A method of determining longitude at sea is that of
the time sight, sometimes called the chronometer method. The altitude of the body
above the sea horizon is measured with a sextant and the chronometer time noted;
the hour angle of the body is then found by the process described in article 316,
Chapter XI.
If the sun is observed, the hour angle is equal to the local apparent time; the
Greenwich apparent tune may be determined by applying the equation of time to the
Greenwich mean time as shown by the chronometer; the longitude is then equal to
the difference between the local and the Greenwich apparent times, being east when
the local time is the later and west when it is the earlier of the two.
If any other celestial body is employed, the hour angle from the local meridian,
found from the sight, is compared with the hour angle from the Greenwich meridian to
obtain the longitude; the Greenwich hour angle is found by converting the Greenwich
mean time into Greenwich sidereal time in the usual manner, and then taking the
difference between the latter and the right ascension of the body, the remainder being
marked east or west, according as the Greenwich sidereal time is the lesser or greater
of the two quantities; and as the local hour angle may be marked east or west accord
ing to the side of the meridian upon which it was observed, the name of the longitude
wul be indicated in combining the quantities.
342. As has been stated, the most favorable position of the celestial body for
finding the hour angle from its altitude is when nearest the prime vertical, provided
the altitude is not so small as to be seriously affected by refraction.
343. In determining the longitude at sea by this method, it is necessary to
employ the latitude by account. This is seldom exactly correct, and a chance of
error is therefore introduced in the resulting hour angle; the magnitude of such an
error depends upon the position of the body relative to the observer. The employ
ment of the Sumner line, which is to be explained in a later chapter, insures the navi
gator against being misled by this cause, and its importance is to be estimated
accordingly.
EXAMPLE: At sea, May 18, 1916, a. m.; Lat. 41 33 N.; Long. 33 37 W., by D. R., the following
altitudes of the sun s lower limb were observed, and times noted by a watch compared with the Green
wich chronometer. Chro. corr., + 4 m 59V2; I. C., -30"; height of the eye, 23 feet; C-W, 2 h 17 m 06 s .
Required the true longitude.
W. T.
Mean,
c-w,
Chro. t.,
Eq. t.,
G. A.T.,
7h 20 15
20 47
21 14
7 20 45.3
+ 2 17 06
9 37 51 .3
3 44.1
-
21 46 34.6
Obs. alt. 0,29 35 30"
46 10
Dec., 17d 20^,19 30 .3 * N.
Eq.t.,17d 20^, 3"> 44.3
Corr.,
ft,
h,
L,
p y
s,
s-h,
Corr., + 9 04"
29 50 04"
41 33 00
70 28 42
2)141 51 46
70 55 53
41 05 49
H. D., +
G. M. T.,
.6
H.D.,
G. M. T.,
Corr.,
l > .7
Corr., +
i -Q?
- 0.17
Dec., 19
31 18" N.
Eq. t.,
3> 44.l
sec., .12588
cosec., .02571
cos.,
Bin.,
G. A. T., 21 h 46 m 34.6
L. A. T., 19 32 05 .5
9.51415
9.81779
2)19. 48353
sin. \ t, 9. 74176
Long.,
2 h 14 m 29M
33 o 37 , 16 //
W
W.
LONGITUDE.
143
EXAMPLE: At sea, April 16, 1916, p. m., in Lat. 11 47 S., Long. 20 E., by D. R., observed an
Ititude of the star Aldebaran, west of the meridian, 23 13 20"; chronometer time, 6 h 58 m 29 s , chro-
ometer fast of G. M. T., 2 m 27 s ; I. C.,-2 00"; height of eye, 26 feet. What was the longitude?
Chro. t.,
6 h 58 m 29 s
9 27
Obs. al
Corr.,
h,
(Tab. <
Corr..
23 04
11 47
106 20
:t. >|c, 23
13 20" R. A. >|c, 4 h 31 m 06 s . 8
G. M. T.,
RA M t S
Drr ifi ry R X/ "M
6 56 02
r-1 37 11
1- 1 09
23
01 05 -. - . .
Red. (Tab. 9), -
G. S. T.,
R. A. *,
H. A. from Gr.,
16), -
7 15"
2 00
8 34 22
4 31 07
05"
00
36
9 15
sec . 00925
cosec . 01791
cos 9. 52141
sin 9. 86783
4 03 15 W.
L,
P,
Jli,
Gr. H. A.
H.A.,
Long.,
2)141
11
41
70
47
35
31
50
45
, 4*
4
03"
05
L 15 S W.
42 W.
2)19. 41640
sin t 9. 70820
/ O h
1
02 m
36
27 s \ r
45"/
EXAMPLE: At sea, July 26, 1916, a. m., in Lat. 25 12 S., Long. 75 3(K W., by D. R., observed an
Ititude of the planet Jupiter, east of the meridian, 32 46 10"; watch time, 2 h 48 m 02 s ; C- W, 5 h 05 m 42 s ;
. C.,+2 m 18 s ; I. C.,+1 7 30"; height of eye, 18 feet, Required the longitude.
\7. T.,
C-W,
Chro. t.,
C.C.,
G. M. T., 25^,
R. A. M.S., Oh,
Red. (Tab. 9),
G. S. T.,
R. A. *,
H. A. from Gr.,
5
48 02
05 42
Obs. alt. #
Corr.,
(Tab. 46).
id,
Corr.,
32
25
101
32
46 10"
4 09
R. A.,25dOh, 2h OS>20
Corr. 4- 18
H. D., + 0.9
G.M.T., 19^.9
7
+
53
2
44
18
32
42 01
5 39"
1 30
4 09
01"
00
18
R. A., 2 08 38
Dec. 25dOh, 11 35 . 9 N.
Corr., + 1.4
Corr., +17-.9
H. D., + .07
G.M.T., 19^.9
Corr., + 1 .39
19
+ 8
+
56
11
3
02
26.8
16.5
42
12
37
Dec., 11 37 18" N.
p, 101 37 18"
sec . 04343
cosec . 00900
cos 9. 24983
sin 9. 86456
4
2
10
08
45.3
38
2
02
07.3 W.
fc
P,
sh,
Gr. H.
H. A.,
2)159
31
19
79
47
45
03
40
39
A., 2*
3
00
L 07" W.
15 E.
2)19. 16682
sin}* 9.58341 -.
Long.,
{ 75 35
35 X 30"
CHAPTER XIV.
AZIMUTH,
344. The azimuth of a body has been defined (art. 223, Chap. VII) as the arc
of the horizon intercepted between the meridian and the vertical circle passing through
the body; and the amplitude (art. 224) as the arc measured between the position of
the body when its true altitude is zero and the east or west point of the horizon.
The amplitude is measured from the east point at rising and from the west point at
setting, and, if added to or subtracted from 90, will agree with the azimuth of the
body when in the true horizon. The azimuth is usually measured from the north point
of the horizon in north latitude, and from the south point in south latitude, through
180 to the east or west; thus, if a body bore N. by E., its azimuth would be named
N. lli E. in north, or S. 168J E. in south latitude.
The determination of the azimuth of a celestial body is an operation of frequent
necessity. At sea, the comparison of the true bearing with a bearing by compass
affords the only means of ascertaining the error of the compass due to variation and
deviation; on shore, the azimuth is required in order to furnish a knowledge of the
variation, and is further essential in all surveying operations, the true direction of
the base line being thus obtained.
345. There are various methods of ob taming the true azimuth of a celestial
body, which will be described as follows: (a) Amplitudes, (b) Time Azimuths, (c)
Altitude Azimuths, (d) Time and Altitude Azimuths. A further method, by means
of the Summer line, will be explained later (Chap. XV). Still another operation
pertains to this subject, namely: (e) The determination of the True Bearing of a
Terrestrial Object.
AMPLITUDES.
346. The method of obtaining the compass error by amplitudes consists in
observing the compass bearing of the sun or other celestial body when its center is
in the true horizon, the true bearing, under such conditions, being obtained by a
short calculation. Since the true horizon is not marked by any visible line (differing
as it does from the visible horizon by reason of the effects of refraction, parallax, and
dip), allowance may be made for the difference by an estimate of the eye, or else the
observation may be made in the visible horizon and a correction applied.
347. When the center of the sun is at a distance above the horizon equal to its
own diameter it is almost exactly in the true horizon; at such a time, note its bearing
by compass, and also note (as in all observations for determining compass error)
the ship s head by compass, and the angle and direction of the ship s heel.
Or, note the bearing at the instant at which the center of the body is in the visible
horizon; in the case of the sun and moon, the correct bearing at that time may be
most accurately ascertained by taking the mean of the bearings when the upper and
the lower limbs of the disk are just appearing or disappearing.
348. To find the true amplitude by computation, there are given the latitude, L, ,
and declination, d. The quantities are connected by the formula,
sin Amp. = sec L sin d,
from a solution of which the amplitude is obtained..
To find the true amplitude by inspection enter Table 39 with the declination at
the top and the latitude in the side column; under the former and opposite the latter
will be given the true amplitude. To obtain accurate results, interpolate for minutes
of latitude and declination.
144
AZIMUTH.
145
To reduce the observed amplitude when taken in the visible horizon to what it
would have been if taken in the true horizon, enter Table 40 with the latitude and
declination to the nearest degree and apply the correction there found to the
observed amplitude; the result will be the corrected amplitude by compass, which,
by comparison with the true amplitude, gives the compass error. When the body
observed is the sun, a star, or a planet, apply the correction, at rising in north lati
tude or at setting in south latitude, to the right, and at setting in north latitude or
at rising in south latitude, to the left. For the moon, apply half the correction in
a contrary direction.
EXAMPLE: At sea, in Lat. 11 29 / N., the observed bearing of the sun, at the time of rising, when
its center was estimated to be one diameter above the visible horizon, was E. 31 N.; corrected
declination 22 32 N. Required the compass error.
By computation.
By inspection (Table 39).
L 11 29
d 22 32
sec
sin
True amp.
Obs. amp.
Error,
E. 23 01 N. sin
E. 31 00 N.
7 59 E.
. 00878
9. 58345
9. 59223
L, 11. 5 N.
d, 22 . 5 N.
Obs. amp.
Error,
E. 23. ON.
E. 31 .ON.
8.OE.
EXAMPLE: At sea, in Lat. 25 03 S., the observed bearing of Venus, when in the visible horizon at
rising, was E. 18 30 7 N., its declination being 21 44 N. Required the compass error.
By computation.
By inspection (Table 39).
L 25 03
d 21 44
sec .04290
sin 9.56854
True amp. E.24 08 N.sin 9.61144
Comp. amp. E. 18 48 N.
Error,
5 20 7 W.
L,
d,
Obs. amp.
Corr. (Tab. 40)
Error,
21 7 N*
True
- 24 -
- 18
5. 3 W.
EXAMPLE: At sea, in Lat. 40 27 N., the mean of the observed bearings of the upper and lower
limbs of the moon, when in contact with the visible horizon at setting, was W. 17 S. ; declination, 21 12 S.
What was the error of the compass?
By computation.
40 27
21 12
sec . 11863
sin 9. 55826
By inspection (Table 39).
U 9 ^ } True amp. W. 28. 4 S.
True amp. W. 28 22 S. sin 9. 67689
Comp. amp. W. 16 42 S.
Error,
11 40
Error,
11. 7 W.
TIME AZIMUTHS.
349. In this method are given the hour angle, t } at tune of observation, the
polar distance, p, and the latitude, L; to find the azimuth, Z.
Any celestial body bright enough to be observed with the azimuth circle may
be employed for observation ; the conditions are, however, most favorable for solu
tion when the altitude is low.
350. Take a bearing of the object, bisecting it if it has an appreciable disk,
and note the time with a watch of known error. Record, as usual, the ship s head
by compass and the amount of heel. If preferred, a series of bearings may be taken
with their corresponding tunes, and the means taken.
351. First prepare the data as follows:
(a) Find the Greenwich time corresponding to the local time of observation.
(b) Take out the declination of the body from the Nautical Almanac; if the
method of computation is employed, the polar distance and the co-latitude should
be noted.
(c) Find the hour angle of the body by rules heretofore given.
61828 16 10
146
AZIMUTH.
This having been done, the true azimuth may be determined either by Time
Azimuth Tables, by the graphic method of an Azimuth Diagram, or by Solution of
the Astronomical Triangle. Owing to the possibility of more expeditious working,
either of the first-named two is to be considered preferable to the last, and the
navigator is recommended to supply himself with a copy of a book of Azimuth
Tables, such as published by the Hydrographic Office, or with an Azimuth Diagram
such as Weir s or Sigsbee s; an explanation of the method of use accompanies each
of these.
352. To solve the triangle:
Let S = J sum of polar distance and co-Lat.
D = J difference of polar distance and co-Lat.
\t \ hour angle.
Z = true azimuth.
Then, tan X = sin D cosec S cot t;
tan Y = cos D sec S cot \ t;
Z=X+Y, orX~Y.
First Case. If the half -sum of the polar distance and co-Lat. is less than 90:
take the sum of the angles X and Y, if the polar distance is greater than the co-Lat. ;
take the difference, if the polar distance is less than the co-Lat.
Second Case. If the half -sum of the polar distance and co-Lat. is greater than
90: always take the difference of X and Y, which subtract from 180, and the result
will be the true azimuth.
In either case, mark the true azimuth N. or S. according to the latitude, and
E. or W. according to the hour angle. It may sometimes be convenient to use the
supplement of the true azimuth, by subtracting it from 180 and reversing the
prefix N. or S., in order to make it correspond to the compass azimuth when the
latter is less than 90.
The cotangent of half the hour angla may be found from Table 44 abreast the
whole hour angle in the column headed "Hour P. M."
EXAMPLE: At sea, in Lat. 30 25 N., Long. 5 h 25 m 42 W., the observed bearing of sun s center was
N. 135 30 E., and the Greenwich mean time, December 3, 2 h 36 m 11". The corrected declination of the
sun was 22 07 S.; the equation of time (additive to mean time), 10 m 03 s . Required the error of the
compass.
G.M.T.(Dec.3), 2 h 36 m 11- co-Lat., 59 35
Long.,
- 5 25 42 p,
112 07
L.M.T.(Dec.2), 21 10 29
Eq. t., + 10 03
L.A.T.,
21 20 32
2 h 39 m 28
p+co-L, 171
S,
42
85 51
2 h 39 m 28
85 51
26 16
50 44
88 19
cot** .44051
cosec . 00114
sin 9. 64596
tan
. 08761
cot it .44051
sec 1. 14045
cos 9. 95267
tan 1. 53363
p-co-L, 52 32 X+Y139 03
D, t 26 16
True azimuth,
Comp. azimuth,
Compass error,
N. 139 03 E.
N. 135 30 E.
3 33 E.
EXAMPLE: At sea, in Lat. 2 16 N., the observed bearing of the sun s center was N. 85 15 E: sun s
hour angle, 3 h 44 m 16% and its declination, 7 38 N. Required the compass error.
co-Lat.,
87
44 /
t
Pi
82
22
S
p+co-L,
170
06
s,
85
03
Y
co-L p,
5
22
Y
3h 44m 16 s
85 03
2 41
5 03
87 22
cot \
cosec
sin
tan
. 27372
. 00162
8. 67039
8. 94573
sec
cos
tan
. 27372
1. 06406
9. 99952
1. 33730
82 19
2 41
True azimuth,
Comp. azimuth,
Compass error,
N. 82 19 E.
N. 85 15 E.
2 56 W
AZIMUTH. 147
EXAMPLE: At sea, in Lat. 16 32 S., observed bearing of Venus N. 56 00 W., its hour angle being
4 b 27 m 31 s , and its declination 23 12 N. What was the error of the compass?
co-Lat.,
73
28
I
4 n 27 m 31 s
cot^t
: . 18022
cot \ i
! . 18022
113
12
S
93 20
cpsec
.00074
sec
1. 23549
~r\
10 50
sin
9 53126
COS
9 97335
p-fco-L,
186
40
-L7 O
X
27 16
tan
9. 71222
s,
93
20
Y
87 40
tan
1. 38906
p co-L,
39
44 /
Y-X
60 24
P,
19
52
Z
119 36
True azimuth,
S. 119
36 W.
Comp.
azimuth,
S. 124
00 W.
Compass error, 4 24 W.
ALTITUDE AZIMUTHS.
353. This method is employed when the altitude of the body is observed at the
same time as the azimuth; in such a case the hour angle need not be known, though
the time of observation should be recorded with sufficient accuracy for the correction
of the declination of the sun, moon, or a planet.
There are given the altitude, h, the polar distance, p, and the latitude, L; to
find the azimuth, Z.
354. Take a bearing of the body by compass, bisecting it if the disk is of
appreciable diameter, and simultaneously measure the altitude; note the time
approximately. . Observe also the ship s heading (by compass) and the heel.
Or a series of azimuths, with corresponding altitudes, may be observed, and the
means employed.
355. Calculate the true altitude and declination from the observed altitude
and the time. Then compute the true azimuth from the following formula:
cos J Z = VGOS s cos (s p) sec L sec Ji,
in which s = % (h+Ij + p). The resulting azimuth is to be reckoned from the north
in north latitude and from the south in south latitude.
It may occur that the term, (s p) , will have a negative value, but since the cosine
of a negative angle less than 90 is positive, the result will not be affected thereby.
EXAMPLE: At sea, in Lat. 30 25 N., the observed bearing of the sun s center was N. 135 3(K E.,
and its corrected altitude 24 59 ; the approximate G. M. T. was 2 h .6, the declination at that time being
22 07 S. Required the compass error.
h 24 59 sec .04267
L 30 25 sec .06431
p 112 07
2 ) 167 31 True azimuth, N. 139 00 E.
Comp. azimuth, N. 135 30 E.
s 83 45 cos 9.03690
sp -28 22 cos 9.94445 Compass error, 3 30 E.
2 ) 19. 08833
*Z 69 30 cos 9.54416
Z 139 00
TIME AND ALTITUDE AZIMUTHS.
356. When, at the time of observing the compass bearing of a celestial body,
the altitude is measured and the exact time noted, the true azimuth may be very
expeditiously determined, a knowledge of the latitude being unnecessary.
In view of the simplicity of the computation, this method strongly commends
itself to observers not provided with azimuth tables or diagram.
357. The observation is identical with that of the altitude azimuth (art. 354),
with the exception that the times of observation must be exactly instead of approx
imately noted.
148 AZIMUTH.
358. Ascertain the declination of the body at time of sight, and correct the
observed altitude; compute the hour angle. We then have:
sin Z = sin t cos d sec li,
from which the azimuth may be found.
This method has a defect in that there is nothing to indicate whether the resulting
azimuth is measured from the north or the south point of the horizon; but as the
approximate azimuth is always known, cases are rare when the solution will be in
question.
EXAMPLE: At sea, in Lat. 30 25 N., Long. 5 h 25 m 42 f W., the observed bearing of the sun s center
was N. 135 30 E.; its altitude at the time was 24 59 ; hour angle, 2 h 39 m 28 f (39 52 ), and declination,
22 07 S. Find the compass error. (See example under Altitude Azimuths and first example under
Time Azimuths.)
t 39 52 sin 9.80686 True azimuth, N. 13904 / E.
d 22 07 cos 9. 96681 Comp. azimuth, N. 135 30 E.
h 24 59 sec .04267
Compass error, 3 34 E.
Z S. 40 56 E. sin 9. 81634
TRUE BEARING OF A TERRESTRIAL OBJECT.
359. Thus far, sea observations for combined variation and deviation have been
discussed, but if it becomes necessary, as in surveying, to ascertain the True Bearing
of a Terrestrial Object, or to find the variation at a shore station, more accurate
methods than the foregoing must be resorted to.
The most reliable method is that by an Astronomical Bearing. This consists in
finding the true bearing of some well-defined object by taking the angle between it
and the sun or other celestial body with a sextant or a theodolite, and simultaneously
noting the time by chronometer, or measuring the altitude, or observing both time
and altitude. It should always be noted whether the object is right or left of the sun.
360. By Sextant. Measure the angular distance between the object and the
sun s limb; and if there is a second observer, measure the altitude of the sun at the
same moment and note the time. In the absence of an assistant, first measure the
altitude of the sun; next, the angular distance between the sun and the object; then,
a second altitude of the sun, noting the time of each observation. Also measure the
altitude of the defined point above the sea or shore horizon.
By Theodolite. This instrument is far more convenient than the sextant, for,
being leveled, the horizontal angle between the sun and the object is at once given,
no matter what may be the altitudes of the objects. In case the altitude of the sun
is needed, it may be read accurately enough from the vertical circle, although not as
finely graduated as the limb of the sextant. The error in altitude must, however,
be found by the level attached to the telescope, since it will usually be found to differ
from the levels of the horizontal circle. If, in directing the telescope to the sun, there
is no colored eyepiece, an image of the sun may be cast on a piece of white paper
held at a little distance from the eyepiece, and by adjusting the focus the shadow
of the cross wires will be seen.
It should be understood that any celestial body may be used as well as the sun,
and there are, in fact, certain advantages in the use of the stars; the sun is chosen
for illustration, because it will usually be found most convenient to employ that body.
361. Find the true azimuth of the celestial bod} 7 by one of the methods pre
viously explained in this chapter, and apply to it the azimuth difference, or horizontal
angle between the celestial and the terrestrial body, having regard to the direction
of one from the other.
To find the azimuth difference from sextant observations, change^ the observed
altitudes of the bodies into apparent altitudes by correcting them for index error of
the sextant, dip, and semidiameter; change the observed angular distance into
apparent angular distance, by correcting for index error and semidiameter. Then if
S = J (App. Dist. + App. Alt.O +App. Alt. Object), we have:
cos i Az. Diff. = A / sec App. Alt.O sec App. Alt. Object cos S cos (S App. Dist.)
whence the azimuth difference is deduced.
AZIMUTH.
149
When the theodolite is used, the horizontal angle is given directly. If only one
limb of the sun is observed, it will be necessary to apply a correction for semidiameter
(S. D. Xsec h), but it is usual to eliminate this correction by taking the mean of
observations of both limbs.
EXAMPLE: From a. m. observations, in Lat. 30 25 24" N., Long. 81 25 24" W., obtained the follow
ing data for finding the true bearing of a station:
Watch time, ll h 22 m 36
C-W, 5 21 18
Chro. corr., -f 2 16
Obs. Ang. Dist. >, 117 07 Left.
Obs. 2
Obs. alt. Station,
i. c.,
71 37 20 /x
2(K
zero.
Dec. S., 22 56 27"
Eq.t., + 7 m OO"
S. D., W 17"
Required the true bearing of the object.
W. T.,
C-W,
Chro. t.,
C.C.,
G. M. T.,
Eq. t.,
5
22 m 36"
21 18
2Q,
>,
S. D.,
App. Alt.,
p. & r.,
7>
71
= -
35
-f
37
MMM^
48
16
20 "
*
40
17
f
<*
ft
f*
8 08
22 56
36 03
9 17
170 43
00"
27
37
E.
E.
sin
cos
sec
9. 15069
9. 96422
. 09239
4
+
43 54
2 16
sin
9. 20730
36
04
1
57
13
4
46 10
7 00
36
OS
44
G. A. T., 4 53 10
Long., 5 25 42
L. A. T., 23 27 28
JO* 32 m 32 9
* \8 08 00"
Obs. Anj. Dist.,
G sS. D., +
App. Ang. Dist.,
117 07 00"
16 17
App. Dist.
App Alt.
App. Alt. Obje<
S
S-App. Dist.
i Az. Diff.
Az. Diff.
117 23
36 05
sec 0.09250
sec 0.00001
cos 9.35536
cos 9. 88115
True bearing Q> i O
Az. Diff., 125
43 E.
00 Left.
117 23 17
True bearing object, N. 45
43 E.
2)153 48
76 54
-40 29
62 30
125 00
2)19. 32902 t
cos 9.66451
EXAMPLE: Same date and place and same objects as in the preceding example; measurement made
with a theodolite, angular distance (>, 123 17 X ; object left of sun. Watch time, ll h 16 m 34 s . 5 ; watch slow
of L. A. T., 4 m 53 s .5. Dec. Q, 22 56 7 S. Required the true bearing. (See article 352.)
W. T., ll h
16 m
34 S .5
co-Lat., 59 35 t
O h 38 m 32 s
cot \ t
1. 07435
coti< 1.07435
W.810W,+
4
53 .5
p, 112 56 S
86 15
cosec
.00093
sec 1. 18440
~r\
oft 41
GI n
Q f^^^^A
rr\a Q Q^llO
L. A. T., 23
21
28 .0
p+co-L, 172 31
^Q T-L
bill
tor
79 24
j
797CO
t,
38
32
S, 86 15 Y
89 39
. fZ/OO
\
tan 2. 20985
p-co-L, 53 21 X+Y169 03
D, 26 41
True bearing 0,
X. 169 03 E.
Az. Diff.,
123 17 Left
True bearing object, N. 45 46 E.
CHAPTER XV.
THE SUMNEE LINE,
DESCRIPTION OF THE LINE.
362. The method of navigation involving the use of the Sumner line takes its
name from Capt. Thomas H. Sumner, an American shipmaster, who discovered it
and published it to the world. As a proof of its value, tne incident which led to its
discovery may be related:
"Having sailed from Charleston, S. C., 25th November, 1837, bound for Greenock,
a series of heavy gales from the westward promised a quick passage; after passing
the Azores the wind prevailed from the southward, with thick weather; after passing
longitude 21 W. no observation was had until near the land, but soundings were
had not far, as was supposed, from the bank. The weather was now more boisterous,
and very thick, and the wind still southerly; arriving about midnight, 17th December,
within 40 miles, by dead reckoning, of Tuskar light, the wind hauled SE. true, making
the Irish coast a lee shore; the ship was then kept close to the wind and several
tacks made to preserve her position as nearly as possible until daylight, when,
nothing being in sight, she was kept on ENE. under short sail with heavy gales. At
about 10 a. m. an altitude of the sun was observed, and the chronometer time noted;
but, having run so far without observation, it was plain the latitude by dead reckoning
was liable to error and could not be entirely relied upon.
The longitude by chronometer was determined, using this uncertain latitude,
and it was found to be 15 E. of the position by dead reckoning; a second latitude
was then assumed 10 north of that by dead reckoning, and toward the danger,
giving a position 27 miles ENE. of the former position; a third latitude was assumed
10 farther north, and still toward the danger, giving a third position ENE. of the
second 27 miles. Upon plotting these three positions on the chart, they were seen
to be in a straight line, and this line passed through Smalls light.
"It then at once appeared that the observed altitude must have happened at
all the three points and at Smalls light and at the ship at the same instant."
Then followed the conclusion that, although the absolute position of the ship
was uncertain, she must be somewhere on that line. The ship was kept on the course
ENE., and in less than an hour Smalls light was made, bearing ENE. \ E. and close
aboard.
The latitude by dead reckoning was found to be 8 in error, and if the position
given by that latitude had been assumed correct, the error would have been 8 miles
too far S., and 31 30" of longitude top far W., and the result to the ship might have
been disastrous had this wrong position been adopted. This represents one of the
practical applications of the Sumner line.
The properties of the line thus found will now be explained.
363. CIRCLES OF EQUAL ALTITUDE. In figure 54, if EE E" represent the earth
projected upon the horizon of a point A, and if it be assumed that, at some particular
instant of time, a celestial body is in the zenith of that point, then the true altitude
of the body as observed at A will be 90. In such a case the great circle EE E",
which forms the horizon of A, will divide the earth into two hemispheres, and from
any point on the surface of one of these hemispheres the body will be visible, while
over the whole of the other hemisphere it will be invisible. The great circle EE E",
from the fact of its marking the limit of illumination of the body, is termed the circle
of illumination, and from any point on its circumference the true altitude of the
center of the body will be zero. If, now, we consider any small circle of the sphere,
150
THE SUMNER LINE.
151
BB B", CC C", DD D", whose plane is parallel to the plane of the circle of illumina
tion and which lies within the hemisphere throughout which the body is visible, it will
be apparent that the true altitude of the body at any point of the circumference of
one or these circles is equal to its true altitude at any other point of the same circum
ference; thus the altitude of the body at B is equal to its altitude at B or B", and
its altitude at D is the same as at D or D".
It therefore follows that at any instant of time there is a series of positions on
the earth* at which a celestial body appears at the same given altitude, and these
positions lie in the circumference of a circle described upon the earth s surface whose
center is at that position which has the body in the zenith, and whose radius depends
upon the zenith distance, or what is the same thing upon the altitude. Such
circles are termed circles of equal altitude. It is important to note that an observer
making an instantaneous transit through the latitudes and longitudes passed over
by any rhumb line or loxodromic curve drawn within the hemisphere of illumination,
through the point A, will
experience no astronomical
difference, with reference to
the observed body in the
zenith of A, save an altitude
difference.
364. The data for an
astronomical sight comprise
merely the time, declination,
and altitude. The first two
fix the position of the body
and may be regarded as
giving the latitude and lon
gitude of that point on the
earth in whose zenith the
body is found; the zenith
distance (the complement of
the altitude) indicates the
distance of the observer
from that point ; but there is
nothing to show at which of
the numerous positions ful
filling the required condi
tions the observation may
have been taken. A num
ber of navigators may meas
ure the same altitude of a
body at the same instant
of time, at places thousands of miles apart; and each proceeds to work out his
position with identical data, so far as this sight is concerned. It is therefore
clear that a single observation is not enough, in itself, to locate the point occu
pied by the observer, and it becomes necessary, in order to fix the position, to
employ a second circle, which may be either that of another celestial body or that of
the same body given by an observation when it is in the zenith of some other point
than when first taken; knowing that the point of observation lies upon each 01 two
circles, it is only possible that it can be at one of their two points of intersection;
and since the position of the ship is always known within fairly close limits, it is easy
to choose the proper one of the two. Figure 55 shows the plotting of observations
of two bodies vertically over the points A and A upon the earth, the zenith distances
corresponding respectively to the radii AO and A O.
365. THE SUMXER LIXE. In practice, under the conditions existing at sea, it
is never necessary to determine the whole of a circle of equal altitude, as a very small
portion of it will suffice for the purposes of navigation; the position is always known
within a distance which will seldom exceed 30 miles under the most unfavorable
conditions, and which is usually very much less; hi the narrow limits thus required,
the arc of the circle will practically coincide with the tangent at its middle point,
FIG. 54.
152
THE SUMNER LINE.
and may be regarded as a straight line. Such a line, comprising so much of the circle
of equal altitude as covers the probable limits of position of the observer, is called a
Sumner line or Line of position.
The latter designation has also a more extended meaning, embracing any line,
straight or curved, which forms a locus of the ship s position, whether it be obtained
from observations of celestial bodies or from bearings or distances of terrestrial
objects.
366. Since the direction of a circle at any point that is, the direction of the
tangent must be perpendicular to the radius at that point, it follows that the
Sumner line always lies in a direction at right angles to that in which the body bears
from the observer. Thus, in figure 55,
it may be seen that m m and n n , the
extended Sumner lines corresponding to
the bodies at A and A , are respectively
perpendicular to the bearings of the bodies
OA and OA . This fact has a most im-
FlG. 55.
portant application in the employment of
the Sumner line.
367. USES OF THE SUMNER LINE.
The Sumner line is valuable because it
gives to the navigator a knowledge of all
of the probable positions of his vessel,
while a sight worked with a single assumed
latitude or longitude gives but one of the
probable positions; it must be recognized
that, in the nature of things, an error in
the assumed coordinate will almost invariably exist, and its possible effect should
be taken into consideration; the line of position reveals the difference of longitude
due to an error in the latitude, or the reverse.
Since the Sumner line is at right angles to the bearing, it may be seen that when
the body bears east or west that is, when it is on the prime vertical the resulting
line runs north and south, coinciding with a meridian; if, in this case, two latitudes
are assumed, the deduced longitudes will be the same. When the body bears north
or south, or is on the meridian, the line runs east and west, and becomes identical with
a parallel of latitude; in such a case, two assumed longitudes will give the same
latitude. Any intermediate bearing gives a Sumner line inclined to both meridians
and parallels; if the line agrees in direction more nearly with the meridian, latitude
should generally be assumed and the longitude worked; if it is nearer a parallel, the
reverse course is Usually preferable. The values of the assumed coordinates may
vary from 10 to 1, according to circumstances.
368. The greatest benefit to be derived from the Sumner method is when two
lines are worked and their intersection found. The two lines may be given by
different bodies, which is generally preferable, or two different lines may be obtained
from the same body from observations taken at different times. The position
given by the intersection of two lines is more accurate the more nearly the lines are
at right angles to each other, as an error in one line thus produces less effect upon the
result. When two observations of the same body are taken, the position of the ship
at the time of first sight must be brought forward to thafc at the second in considering
the intersection; if, for ^example, a certain line is determined, and the ship then runs
NW. 27 miles, it is evident that her new position is on a line parallel with the first and
27 miles to the NW. of it ; a second line being obtained, the intersection of this with
the first line, as corrected for the run, gives the ship s position.
Besides the employment of two lines for intersection with each other, a single
line may be made to serve various useful purposes for the navigator. These are
described in article 389, Chapter XVI.
METHODS OF DETERMINATION.
369. ^There are three methods in common use for determining the Sumner line:
(a) THE CHORD METHOD: To assume two values of one coordinate and find the
corresponding values of the other. Two values of the latitude may be assumed and
i
THE SUMNER LINE. 153
the longitudes determined, as was done by Capt. Simmer on the occasion that led to
the discovery of his method; or else two values of the longitude may be assumed
and the latitudes determined. Two points are fixed in this way, and the line joining
them is the Sumner line.
(b) THE TANGENT METHOD: To assume either one latitude or one longitude and
determine the corresponding coordinate. This gives one point of the Sumner line.
The azimuth of the observed celestial body is then ascertained, and a line is drawn
through the determined point at right angles to the direction in which the body bore
at the time of the sight. This will be the Sumner line.
(c) In accordance with the method of Saint Hilaire, to be described in article
371, to lay off from an assumed geographical position, along the line of direction
in which the body bore at the time of the sight, the determined distance to the
Sumner line.
370. It follows that if the Sumner line be located by the first method and its
direction thus defined, the azimuth of the observed body may be determined by
the angle made by the line with the meridian and adding or subtracting 90.
EXAMPLE: At sea, July 26, 1916, a. m., in Lat. 25 12 S., Long. 75 3(X W., by D. R., observed an
altitude of the planet Jupiter, east of the meridian, 32 W 10"; watch time, 2 h 48 m 02 s ; C-W, 5 h 05 m 42 ;
C. C., -f 2 m 18 s ; I. C., 4- I 30"; height of eye, 18 feet. Required the Sumner line.
From a solution of this same problem for a single longitude (art. 343, Chap. XIII), the following
were found: H. A. from Gr., 2 h 02 m 07 s W.; h, 32 42 01 ?; p, 101 37 18". Assume values of Lat.
25 02 and 25 22 S.
h 32 42 01"
Lj 25 02 00 sec . 04284 L 2 25 22 00" sec . 04403
p 101 37 18 cosec .00900 cosec .00900
2)159 21 19
t 79 40 40 cos 9.25330 So 79 50 40 cos 9.24630
i-h 46 58 39 sin 9.86397 sl-h 47 08 39 sin 9.86514
Gr. H. A. 2 h 02 m 07 s W. 2)19. 16911 Gr. H. A. 2 h 02 m 07 s 2)19. 16447
H. A. x 3 00 45 E. sin $ ^ 9.58455 H. A. 2 2 59 44 sin ^ 9.58224
5 h 02 m 52 s 1 w T / 5 h Ol m 51 s
75 o 43/ <,<) JW. Long. 2 { ^ 2?/ 4&/
A comparison of these results with those obtained by the solution with a single
latitude shows that the hour angle, and consequently the longitude, corresponding
to the latitude 25 12 S. are the means of those corresponding to the latitudes here
used; and therefore that the assumption that the Sumner line is a straight line is
accurate.
The line of the same sight might also have been found as follows :
Working with the single latitude 25 12 S., it was found that the corresponding
longitude was 75 35 30" W. Now, by referring to an azimuth table or azimuth
diagram, the azimuth corresponding to Lat. 25.2 S., Dec., 11.6 N., H. A., 3 h 00 m .2
E. is S. 124 30 E.; therefore the Sumner line extends S. 34 30 E.
The line may therefore be defined in either of two ways, thus:
A J25 02 00" S. A /25 22 00" S.
A H75 43 00 W. A2 \75 27 45 W.
n . J25 12 00" S. Line runs S. 34 30 E.
Jr > A 175 35 30 W.
By inspection of the coordinates of A^ and A 2 it may be seen that
+ 20 diff. lat. makes -15 .25 diff. long.; or
+ 20 miles diff. lat. makes - 13.8 miles departure.
Therefore by reference to Table 2 it appears that the line runs about S. 34 30
E., and the azimuth of the body is S. 124 30 E.; thus the results obtained by the
two methods agree.
154 THE SUMNER LINE.
; sea, May 18, 1916, a. m., Lat. 41 33 N., Long. 33 37 W., by D. R., the mean of a
altitudes of the sun s lower limb was 29 41 00"; the mean watch time, 7 h 20 m 45 S .3;
EXAMPLE: At
series of observed
C. C.,+4 m 59 S .2; I. C., -30"; height of the eye, 23 feet; C-W, 2 h 17 m 06 s . Required the Sunrner line.
From a solution of this same problem for a single longitude (art. 343, Chap. XIII) the following
were found: G. A. T., 21 h 46 m 35 s - h 29 50 04": , 70 28 42". Assume values of the latitude 41 03
and 42 03 N.
h 29 50 04"
Lj 41 03 00 sec . 12255 L 2 42 03 00" sec . 12927
p 70 28 42 cosec .02571 cosec .02571
2)141 21 46
s 1 70 40 53 cos 9.51959 S 2 71 10 53 cos 9.50863
Sl -h 40 50 49 sin 9.81560 s 2 h 41 20 49 sin 9.81995
G. A. T., 21 h 46 m 35 s 2)19.48345 G. A. T. 21 h 46 m 35 s 2)19.48356
L. A. T.j 19 32 07 sin ^ 9. 74172 L. A. T. 2 19 32 05 sin $ t 2 9. 74178
/ 2 h 14 m 28 3 \ w / 2 h 14 m 30 s \ w
Long.! | 33 o 37 , 00 //fW. -Long. 2 <^ 37 / 30"}^-
. / 41 03 00" N. A /42 03 00" N. +60 diff. lat, makes+0 .25 long.
AI \ 33 37 00 W. A2 \33 37 30 W. +60 miles diff. lat. makes+0.2 mile departure.
Line runs, N. i W. Azimuth, N. 89f E.
The same site worked with a single latitude, 41 33 N., as was done in the
original example, with azimuth taken irom tables or diagram, gives:
41 33 00" N. Azimuth, N. 89 45 E.
33 37 16" W. Line runs, N. 15 W.
This example illustrates the case in which an observation is taken practically
on the prime vertical; the azimuth shows the bearing to be within 15 of true East,
and the Sumner line is therefore within 15 of the meridian; a variation of 30
in either direction from the dead reckoning latitude makes a difference of only 7". 5
in the longitude.
EXAMPLE: October 10, 1916, in Lat. 6 20 S. by account, Long. 30 21 30" W.; chro. time, 12M5 m 10 s ;
observed altitude of moon s upper limb, 70 15 30", bearing north and east; I. C., 3 00"; height of
eye, 26 feet; chro. fast of G. M. T., l m 37 s . 5. ^ Required the Sumner line.
From a solution of the same problem with a single longitude (art. 332, Chap. XII), the following
values are obtained: H. A. from Greenwich, l h 16 m 51 s W.; h, 70 11 03"; d, 10 03 00" N. Assume
the longitudes 30 10 and 30 30 W.
Gr. H. A.
Long. :
t
l h 16 m 51 s W. Gr. H. A. l h 16 m 51 s
2 00 40 W. Long. 2 2 02 00
f O b 43 in 498
l \10 57 15"
f Qh 45m 093
Hll 17 15"
h
Lat.i
10
10
70
10
16
57
03
11
13
43
15"
00
03
57 N.
30 S.
sec . 00799
tan 9. 24853 cosec
. 75819
9 97349 A i 6 29/ 33 " S "
A H30 10 00 W.
9. 24955
sin
tan 9. 25652 sin
cos
9. 98123
6
29
33 S.
t 2
d
h
11
10
70
17
03
11
15"
00
03
sec . 00848
tan 9. 24853 cosec
. 75819
9.97349 A 2 {; gj"
sin
V*
10
16
14
31
38 N.
00 S.
tan 9. 25701 sin
cos
9. 25002
9. 98170
Lat. 2 6 16 22 S.
THE SUMNER LIXE. 155
Working by the other method, and finding the azimuth, we have:
" Line mns K 55 50 W
It might be shown that the results check with each other, as in previous cases.
EXAMPLE: At sea, July 12, 1916, in Lat. 50 N., Long., 40 W., observed circum-meridian altitude
of the sun s lower limb, the time by a chronometer regulated to Greenwich mean time bein<* 2 h 41 m 39 s -
chro. corr., -2- 30 s ; I. C., -3 0"; height of the eye, 15 feet. Find the Sumner line.
From the solution of the same problem for a single latitude (art. 330, Chap. XII) the following values
were obtained: G. A. T., 2 h 33 m 45 s ; h, 61 57 01"; d, 21 58 38" N.; a (Tab. 26), 2".5. Assume longi
tudes 39 45 and 40 15 W.
Gr. H. A. 2 h 33 m 45 s Gr. H. A. 2 h 33 m 45
Long.! 2 39 00 Long. 2 2 41 00
^ 5 15 t 2 7 15
h 61 57 01" h 61 57 01"
atf + 1 09 at, 2 + 2 11
H, 61 58 10 H 2 61 59 12
z l 28 01 50 N. z 2 28 00 48 N.
d 21 58 38 N. d 21 58 38 N.
L! 50 00 28 N. L 2 49 59 26 N.
The line given by these coordinates is then:
A
J50 0<y 28" N. * /49 59 26" X.
H39 45 00 W. A2 \40 15 00 W.
This shows that the Sumner line lies so nearly in a due east-and-west direction
that a difference of longitude of 30 makes a difference of latitude of only 1 .
From the azimuth tables or diagram, it is found that the azimuth of the sun
corresponding to Lat. 50 N. Dec. 22 N. and H. A. 6 m 15 s E., is N. 176 55 E.
Therefore, using the values given by the earlier solution, the line is defined as follows:
A )49 59 59" N. T . X T Rfi0 / F
A \40 00 00 W. Lme runs N 8 55 -k
The direction of the line thus given and of the one found from the double co
ordinates may be shown to agree as in examples before given.
THE METHOD OF SAINT HILAIBE OB OF THE CALCULATED ALTITUDES.
371. The forego ing parts of this work have set forth that, when the purpose
of the navigator is to find the latitude, the observed celestial body should be situated
on or near the meridian or at least not remote from it, and that he must apply different
rules according as the body is on or near or more remote from the meridian; and
again when his purpose is to find the longitude, the observed celestial body should
be situated on or near or at least not remote from the prime vertical, and that he
must then apply another set of rules. It is also explained in article 363 that a navi
gator, who has measured the altitude of a celestial body at a known instant of time,
has really located his geographical position on the circumference of a circle whose
radius is equal to the zenith distance (90 Alt.) and whose center is the geographical
position of the celestial body or that point on the earth s surface which falls vertically
under the observed body at the instant of observation.
It has been pointed"out that practical needs are concerned only with that portion
of the circumference of the circle of position which lies in the vicinity of the estimated
position of the ship, and, having seen how this portion may be determined and laid
down by methods depending upon the computation of latitudes and longitudes, we
proceed to extend our view to the accomplishment of this purpose by a method which
is now rapidly growing in favor among practical navigators, because it brings the
whole of astronomical navigation under a single rule by rendering the course of
Erocedure the same, whatever the situation in the heavens of the observed body may
e, provided only that the conditions admit of accurate measurement of its altitude.
156 THE SUMNER LINE.
In figure 54, the circumference of a circle of position is represented as having
been laid down from A, the geographical position of the observed body, as a center,
with a radius AC equal to the zenith distance of the observed celestial body; but it
is evident that a small arc of the circumference, not differing sensibly from a straight
line within the extent of a Sumner line, may be determined in the following manner
from a neighboring geographical position, as at P, inside or outside of the circum
ference and at or near the position of the ship as given by dead reckoning :
1. Find the great-circle distance (zenith distance) and bearing (azimuth) of the
geographical position of the observed body A from the observer s assumed position P.
2. Take the difference, in minutes of arc (nautical miles), between this zenith
distance AP due to the observer s assumed position, and the zenith distance AC
found from the true altitude resulting from observation.
3. Lay off this difference, which is called the altitude-difference, or intercept,
from the assumed position P either away from or toward the observed celestial body
according as the true altitude by observation is less or greater than the altitude at
the assumed position, and through the point thus reached draw a line at right angles
to the bearing.
The line so drawn^will evidently be a tangent to the circumference of the circle
of position, and will be so nearly coincident with this circumference throughout such
length as the Sumner line need have, in all those cases in which the zenith distance
is as great as 10, that the tangent itself may be taken as the true line of position.
Obviously the only trigonometrical computation that occurs under this method is
in calculating the length and bearing of the great-circle arc joining the position P,
which is assumed or known from the dead reckoning, with the geographical position
A, which is always in a latitude equal to the declination of the observed celestial
body at the instant of observation and in a longitude equal to the hour angle of the
body from the prime meridian (Greenwich). In the case of the sun the Greenwich
hour angle is expressed, by Greenwich apparent time, and in the case of any other
celestial body the Greenwich hour angle is found as explained in article 293, using
G. M. T. instead of L. M. T.
372. Being strictly in the nature of calculating the great-circle distance and
course between two points whose latitudes and longitudes are given, these compu
tations may be made according to articles 190 and 191, Chapter V; but in practice
it is unnecessary to do so, since various altitude and azimuth tables give the distance
and azimuth or true bearing, on the globe or on the celestial sphere, of any place from
every other place, and consequently the altitude and azimuth, or zenith distance and
bearing, that any celestial body would have at any given time to an observer situated
in any given geographical position. So that an observer in a geographical position
as yet unknown, about to measure the altitude of a celestial body for the purpose
of deducing geographical position, may assume beforehand a geographical position
in the region of his station and find from the tables the altitude and azimuth which
the celestial body would have if observed from the assumed position; and then,
comparing the altitude so taken from the tables with the true altitude obtained by
measurement, may at once find the Sumner line by laying off from the assumed geo
graphical position along the direction of the bearing an intercept, called the altitude-
difference, and drawing through its extremity a line at right angles to the bearing.
After finding the altitude-difference or intercept, the simplest procedure consists
in laying it off on the chart from the assumed position and drawing the Sumner line
through its extremity, but if, for any reason, this process is not desirable, the latitude
and longitude of the extremity of the intercept, which is a point on the Sumner line,
called the " computed point," may be found by the use of the Traverse Tables, or
may be computed directly.
The exact position of the observer on the Sumner line is, of course, indeterminate
from one observation, unless either the latitude or longitude of the observer s position
be known beforehand, but the computed point will always be nearer to the actual
position of ^the observer than the dead reckoning or assumed position is. To obtain
a fix, that is, to find the actual position, it is necessary to determine the intersection
of the first Sumner line with another line of position, which may be another Sumner
line or a line of bearing or any other line containing the ship s position at the same
time.
THE SUMNER LINE. 157
When the specially prepared altitude and azimuth tables are not preferred, the
required azimuth or true bearing of the observed celestial body may be taken from
the time azimuth tables, and the zenith distance, and hence the altitude, that the
observed body would have at the instant of observation to an observer in the
assumed geographical position may be conveniently computed by the following
formula :
hav z = hav (L ~ d) + cos L cos d hav t
or by the formula of haversines, which is rid of all doubt as to the algebraical signs
of the quantities and requires reference to only one trigonometrical table:
hav z = hav (Co. L-P. D.) + {hav (Co. L + P. D.)-hav (Co. L-P. D.)}hav t
These are modifications of the fundamental formula:
sin 7i = sin L sin d + cos L cos d cos t,
which is itself often preferred for the computation of the altitude from the latitude,
declination, and hour angle.
In the computations which follow, the parts of the several formulae have been
designated as follows:
IN THE COSINE-HAVERSINE FORMULA :
hav 6=coB L cos d hav t; /
hence,
hav z=hav (L~cT)+hav 6
IN THE HAVERSINE FORMULA:
hav A=hav (Co. L+P. D.)-hav (Co. L-P. D.)
hav B = {hav (Co. L+P. D.) hav (Co. L-P. D.)} hav t;
hence,
hav 2=hav (Co. L-P. D.)+hav B.
IN THE SINE-COSINE FORMULA:
A=sin L sin d< B=cos L cos d cos t;
hence,
sin ft=A+B.
EXAMPLE: At sea, May 18, 1916, a. m., Lat. 41 33 N.; Long. 33 37 W., by D. R., the mean of a
series of observed altitudes of the sun s lower limb was 29 41 00"; the mean watch time, 7 h 20 m 45. 3 f ;
C. C., +4 m 59.2; I. C., -30"; height of eye, 23 feet; C.-W., 2 h 17 m 06 s . Required the Sumner line.
From a solution of the same problem under article 343. Chapter XIII, and article 370, Chapter XV, the
following are taken from among the prepared data: G. A. T., 21 h 46 m 35 s ; P. D. . 70 28 42"; h, 29 50 04",
and, therefore, the measured zenith distance (90 -ft), 60 09 56".
Assume a position in latitude 41 30 N. and longitude 33 38 45" or 2 h 14 m 35 s W.. then the solution
will be as follows:
L. 41 30 00" G. A. T. 21* 46 ra 35 s
Long. 2 14 35 W.
Co. L. 48 30 00
P. D. 70 28 42 L. A. T. 19 32 00 =t.
NOTE. After obtaining the G. A. T., it will be seen that the longitude of the assumed position may
be so chosen as to avoid seconds in the L. A. T. or H. A.
The azimuth found from the azimuth tables is N. 89 45 E. ^r~
BY THE COSIXE-HAVERSINE FORMULA:
t 19 h 32 1 " 00 log hav 9. 48378
L 41 30 00" N. log cos 9.87446
d 19 31 18" N. log cos 9. 97429
log hav 6 9. 33253
nat hav 6 0. 21505
21 58 42" nat hav 0. 03634
Calculated z 60 11 00" nat hav 0. 25139
90 OCK 00"
Calculated h 29 49 00
Observed ft 29 50 04
Altitude-difference 1 04
a The arrangement of Table 45 is such as to obviate the necessity of taking out the value of the angle in finding the natural
haversine from the log. haversine, or vice versa.
158
THE SUMNEK LINE.
BY THE HAVERSINE FORMULA:
Co. L+P. D. 118 58 42" nat hav 0. 74225
Co. L-P. D. 21 58 42 nat hav 0.03634
nat hav A
log hav A
log hav t
log hav B
nat hav B
nat hav (Co. L P. D.)
nat hav z
Calculated z
Calculated h
Observed h
Altitude-difference
BY THE SINE-COSINE FORMULA:
t 19 h 32 m OO s
293 00 00"
L 41 30 00 N.
d 19 31 18 N.
0. 70591"
9. 84876
9. 48378
9. 33254
0. 21505
0. 03634
0. 25139
60 11 00"
90 00 00
29 49 00
29 50 04
1 04
log sin 9. 82126
log sin 9. 52396
log cos 9. 87446
log cos 9. 97429
log A 9. 34522
A 0. 22142
log B 9. 44063
B 0. 27581
A 0. 22142
Calculated A=29 49 00" nat sin=A+B
0. 49723
Since the observed altitude is higher than the calculated altitude, the observer s
position is nearer to the observed body than the assumed position. Consequently
the altitude-difference should be laid off in a direction to the east and north, 89 45 ,
1.0 nautical mile from the assumed position.
Or, by the Traverse Tables :
Course.
Distance.
Difl. Lat.
Dep.
Diflf. Long.
89 45
1.0
/ .ON.
1 . E.
1 . 3 E.
Assumed position, Lat.
Diff. Lat.
41 30 00" N.
00 N.
Computed point on Sumner line, 41 30 00" N.
Long. 33 38 45" W.
Diff. Long. 1 18 E.
33 37 27" W.
The direction of the Sumner line, being at right angles to the azimuth or true
bearing of the observed celestial body, runs N. 15 W. and S. 15 E. or 359 45
and 179 45 .
EXAMPLE: At sea, October 10, 1916, in Lat. 6 20 S. by account, Long. 30 21 30" W.; chro. time,
12 h 45 m 10 s ; observed altitude of moon s upper limb, 70 15 30", bearing north and east; I. C., -3 00";
height of eye, 26 feet; chro. fast of G. M. T., l m 37 s . 5. Required the Sumner line.
From a solution of the same problem under article 332, Chapter XII, and again under article 370,
Chapter XV, the following quantities are taken from among the prepared data: H. A. from Greenwich,
l h 16 m 51 s W.; corrected altitude, ft, 70 11 03"; d, 10 03 00" N. and, hence, P. D., 79 57 00".
Assume a position in Lat. 6 00 S. and Long. 30 27 45" W.; then the solution will be as follows:
L 6 00 00" S. Gr. H. A. l h 16 m 51 s W.
Long. 2 01 51 W.
Co. L 96 00 00
P. D. 79 57 00 t- 45 00
o The arrangement of Table 45 is such as to obviate the necessity of taking out the value of the angle in finding the natural
haversine from the log. haversine, or vice versa.
THE SUMNER LINE.
159
BY THE COSINE-HAVERSINE FORMULA :
Calculated h
Observed h
Altitude-difference
BY THE HAVERSINE FORMULA
0* 45 m OO s
6 00 00" S.
10 03 00 N.
16 03 00 //
19 34 30
90 00 00
70 25 30
70 11 03
14 27
log hav 7. 98260
log cos 9. 99761
log cos 9. 99328
log have 7.97349
nat hav 6 0. 00941
nat hav 0. 01949
nat hav 0. 02890
Co. L-f P. D. 175 57 00" nat
Co. L-P. D. 16 03 00 nat
nat hav A
log hav A
log hav t
log hav B
nat hav B
nat hav (Co. L-P. D.)
nat hav z
Calculated z
Calculated h
Observed h
hav 0.99875
hav 0. 01949
0. 97926
9. 99090
7. 98260
Altitude-difference
BY THE SINE-COSINE FORMULA I
t O h 45 m OO s
11 15 00"
L 6 00 00 S.
d 10 03 00 N.
7.97350
0.00941
0. 01949
0. 02890
19 34 30"
90 00 00
70 25 30
70 11 03
14 27
log sin 9. 01923-
log sin 9. 24181
log A 8.26104-
A =-0.01824
.log cos 9.99157
log cos 9. 99761
log cos 9. 99328
log B 9. 98246
B =0. 96044
A =-0.01824
Calculated h=70 25 30" nat. sin=A+B 0. 94220
The azimuth from the Azimuth Tables S. 145 5^ E. or N. 34 W E.
Since the observed altitude is lower than the calculated altitude, the observer s
position is further removed from the observed body than the assumed position.
Consequently the altitude-difference should be laid off to the south and west, 214
14.4 nautical miles from the assumed position.
Or, by the Traverse Tables:
Course.
Distance. .
Diff. Lat.
Dep.
j Diff. Long.
214
14.4
11 .9 S.
8 .0 W.
8 .0 W.
i
Assumed position, Lat.
Diff. Lat
6 W 00" S.
11 54 S.
Computed point on Sunnier line, 6 11 54 S.
Long. 30 27 45" W.
Diff. Long. 8 00 W.
30 35 45 W.
160
THE SUMNER LINE.
The direction of the Sumner line, being at right angles to the azimuth or true
bearing of the observed body, is N. 55 50 W. and S. 55 50 E., or 304 10
and 124 10 .
EXAMPLE: At sea, July 12, 1916, in Lat. 50 N., Long. 40 W., observed an ex-meridian altitude of
the sun s lower limb, 61 48 30", the time by chronometer regulated to Greenwich mean time being
2 h 41 m 39 8 ; chro. corr., 2 m 30 s ; I. C., 3 00"; height of eye, 15 feet. Find the Sumner line.
From a solution of the same problem under article 330, Chapter XII, and again under article 370,
Chapter XV, the following quantities are taken from among the prepared data: G. A. T., 2 h 33 m 45 s ; h,
61 57 01"; d, 21 58 38" N.
Assume a position in Lat. 49 50 7 N., Long. 40 11 15" or 2 h 40 m 45 s W., then the solution will be
as follows:
L.
49 50 00" N.
Co. L 40 10 00
P. D. 68 01 22
G. A. T.
Long.
2 b 33 m 45 s
2 40 45 W.
L. A. T=t 07 00 E.
BY COSINE-HAVERSINE FORMULA:
d 21 58 38" N.
P. D. 68 01 22
Calculated h
Observed h
Altitude-difference
O h 7 m 00 s
49 50 00" N.
21 58 38" N.
27 51 22"
27 53 15"
90 00 00"
62 06 45
61 57 01
9 44
log hav 6. 36774
log cos 9. 80957
log cos 9. 96724
log hav 6 6. 14455
nat hav d 0. 00014
nat hav 0. 05793
nat hav 0. 05807
BY HAVERSINE FORMULA:
Co. L+P. D. 108 11 22"
Co. L-P. D. 28 11 22
nat hav A
log hav A
log hav t
log hav B
nat hav B
nat hav (Co. L P. D.)
nat hav z
Calculated z
Calculated h
Observed h
Altitude-difference
nat hav 0. 65607
nat hav 0. 05793
0. 59814
9. 77681
6. 36774
6. 14455
0. 00014
0. 05793
0. 05807
27 53 15"
90 00 00
62 06 45
61 57 01
9 44
BY THE SINE-COSINE FORMULA:
t O h 07 m OO s
1 45 00"
log cos
9. 99980
L 49 50 00 N.
d 21 58 38 N.
log sin
log sin
9. 88319
9. 57315
log cos
log cos
9. 80957
9. 96724
log A
A
9. 45634
0. 28598
,ogB
A
9. 77661
0. 59787
0. 28598
Calculated fc=62 06 37"
nat sin =
The azimuth from the Azimuth Tables: N. 177 E. or S. 3 E.
A+B 0. 88385
THE SUMNER LINE.
161
Since the observed altitude is lower than the calculated altitude, the observer s position is farther
removed from the observed body than the assumed position. Consequently the altitude-difference
should be laid oft to the north and west, 857, 9.7 nautical miles from the assumed position
Or, by the Traverse Tables:
Course.
Distance.
Diff. Lat.
Dep.
Diff. Long.
357
9.7
9.7 N.
(X.5 W.
(X.78 \V.
Assumed position, Lat.
Diff. Lat.
49 50 00" N.
9 42 N.
Long.
Diff. Long.
40 C
11
15" W.
46 W.
Computed point of Sunnier line 49 59 42 N.
40 12 01 W.
The direction of the Sumner line, being at right angles to the azimuth or true bearing of the observed
body, is N. 87 E. and S. 87 W., or 87 and 267.
373. In the first of the three foregoing examples, the observed celestial body is
represented as being near the prime vertical; in the second, remote from both the
prime vertical and the meridian; and in the third, near the meridian. These examples
have been solved in the preceding chapters by three different methods known,
respectively, as the time sight, the < d>", and the ex-meridian; but we have here
treated all of them by one method, and have determined Sumner lines which are in
agreement with those determined by the various preceding methods. And it would
be likewise if we should take examples in which meridian altitudes have been observed.
Inasmuch as the local hour angle of a celestial body is at the time of its passage
across the meridian of an observer, the second member of the right-hand side of the
equation of haversines becomes zero in cases in which the meridian altitude has
been observed, since the haversine of Q is equal to zero. The equation therefore
reduces to
havz = hav (Co. L-P. D.)
or
z= (Co. L-P. D.)
which leads at once to the usual formulae given in article 321, Chapter XII, for
finding the latitude from a meridian altitude. By this we are taught the full inter
pretation of a meridian altitude, which is that it gives the latitude of the intersection
with the local meridian of a Sumner line coinciding with a parallel of latitude.
374. In addition to the simplicity which arises from always working by the
same rule, the navigator has, by this method, the further practical advantage of being
able to do the most of the work of obtaining the Sumner line before taking the
observation, since, in clear weather, he may, in selecting the assumed geographical
position, assume an hour angle and calculate what time the chronometer or watch
ought to show at the instant when the celestial body has this hour angle, and then
observe the altitude at this instant; or, if anything sfiould happen to make him a few
seconds late in getting the altitude, he may alter the assumed longitude by a corre
sponding amount so as to make the hour angle right, and then the rest of the work
will hold good.
After correcting the observed altitude and obtaining from it the true altitude,
no more time need subsequently elapse in determining the Sumner line than is
necessary to take the difference between the altitudes found by calculation and by
observation and to rule a line at right angles to the bearing of the observed body
through the point found by laying off this altitude-difference as an intercept from the
assumed position.
375. It has already been remarked that the labor of performing such computa
tions as the foregoing may be saved when a book of altitude and azimuth tables is
at hand. These tables are arranged to be entered with the hour angle, the declina
tion, and the latitude; and they contain the corresponding values of the altitude
and azimuth. In the various books containing such tables, the special rules to be
observed in their use are set forth.
61828 16 11
162 THE SUMNER LINE.
It has been implied that when the altitude of the observed body is greater than
80 and, therefore, the zenith distance or radius of the circle of position is less than
10, the tangent drawn to the circumference to represent the Sumner line could no
longer be regarded as coinciding throughout its proper length with the arc of the
circumference. When the zenith distance is 10, the departure of the tangent from
the circumference is one-tenth of a mile at a distance of 10 miles from the theoretical
point of tangency and seven-tenths of a mile at a distance of 30 miles from the
theoretical point of tangency. These departures are doubled when the zenith distance
is reduced to 5 Q , and they are nearly ten times the amounts stated for 10 when the
zenith distance is shortened to 1 Q .
There is not, however, any occasion for resorting to the proceeding of laying
down a straight line as a substitute for an arc of the actual circle of position when
the zenith distance is only a few degrees in length. In such cases the greatest con
venience and the best results are found by drawing circles of position directly on the
navigator s chart. For this purpose the polyconic chart, being issued to navigators
throughout all latitudes from 20 to 60 north of the Equator in connection with the
works of the United States Coast and Geodetic Survey, and therefore being available
throughout a like extent of south latitude by mere inversion, is generally serviceable,
because a chart embracing any certain parallels of latitude is available between these
parallels of latitude throughout all longitudes; and the Mercator projection may also
be used for this purpose within the Tropics, since the length of a minute of latitude
as represented on this projection varies but little within tropical limits. For instance,
it happens in crossing the tropical zone that, for a day or so, the sun is very near the
zenith perhaps not more than 1 Q away on one day and 2 Q or 3 on another. In
such circumstances, having a chart of suitable scale embracing the parallels of latitude
of the region in which the ship is situated, plot the sun s geographical position with
Greenwich hour angle as longitude and declination as latitude, take on the dividers the
zenith distance, or complement of the corrected altitude, and draw in a portion of
the circumference of the actual circle of position lying near the position of the ship
as given by dead reckoning. Then wait until the azimuth has changed 30 or so
which it does very rapidly near noon and draw a second similar arc. The inter
section of these arcs gives the ship s position with accuracy. Of course if the ship
has moved in geographical place in the interval between the two sights, it will be
necessary, in order to find the geographical position at the instant of the second sight,
to move the first circle of position in direction and amount equal to the course and
distance made good in the interval.
FINDING THE INTERSECTION OF STJMNEB LINES.
376. The intersection of Sumner lines may be found either graphically or by
computation.
(a) GRAPHIC METHODS. Each line may be plotted upon the chart of the locality
in which the ship is being navigated, in accordance with the data for its determination
(see art. 367), and the intersection thus found. This plan will commend itself
especially when the vessel is near shore, as the chart in use will then probably be
one of large enough scale, and it will be an advantage to see where the Sumner lines
fall with reference to the soundings and landmarks. To aid the extension of this
convenient practice on the ocean, where the navigator is usually furnished only with
a general chart, position-line plotting sheets have been provided for the use of navi
gators upon an ample scale.
(b) METHODS BY COMPUTATION. The finding of the intersection of two Sumner
lines by computation may be divided into two cases:
Case I. When one line lies in a NE.-SW. direction, and the other in a NW.-SE.
direction, as shown in figure 56.
Case IL When both lie in a NE.-SW., or both in a NW.-SE. direction, as shown
in figure 57.
377. If each Sumner line is defined by the latitude and longitude of one of its
points and the azimuth of the celestial body at right angles to whose true bearing the
line runs, we may then, by means of Table 47, find the longitude of any other point
on such a line when its difference of latitude from the known point has been ascer-
THE SUMXER LINE.
163
tained. The numbers in Table 47 are values of the longitude factor, usually denoted
by the letter F. They vary with the latitude of the observer and the celestial body s
azimuth at right angles to the direction of the line, and express the change in longitude
due to a change of 1 in latitude along any given Sumner line. So that the difference
of latitude between any two points of a line, being multiplied by the longitude factor,
will give the difference of longitude between those points.
Turning to figures 56 and 57 and considering the Sumner lines A 1 A 2 and B t B 2
there represented to be defined by the azimuth at right angles to each and the lati
tudes and longitudes of the points A t and B t , respectively, we proceed to show the
relations which exist for determining the latitude and longitude of the fix at their
intersection by means of the tabulated longitude factors. The line PO being drawn
perpendicular to the parallel of latitude through the points A l and B 1? the latitude
of the intersection will be a distance OP from the common latitude of A and B 1? and
its longitude will be a distance A 1 O from A t and B t O from B t . Let Y 1 and F 2 repre
sent the longitude factors from Table 47 for the Sumner lines Aj A 2 and B t B 2 ,
respectively. Then, since Fj is the difference of longitude corresponding to a change
of 1 of latitude along the line A x A 2 , the difference of longitude A t O must be equal
to F x multiplied into the number of minutes of latitude in the length OP. Therefore,
and likewise
A 1 O = OPxF 1 ,
B 1 = OPxF 3 ;
and, since the known difference of longitude between the points A t and B x is com
posed of the sum of A t O and B t O in Case I, and the difference of Aj O and E 1 O in
Case II, we have
A,
= A X B^
+ OPxF^OP (F^F,), in Case I, and
^OP (^-F,), in Case II.
thus:
From which, placing the known quantities on the right-hand side of the equations,
OP = T-, in Case I, and
"~
in Case II.
and Bj
etween
Hence, we obtain the difference of latitude from the common parallel of A l
to the point of intersection by dividing the known difference of longitude b
the points A t and B t by the sum of the longitude factors of the respective Sumner
lines in Case I, and by their difference in Case II.
Having determined OP and hence the latitude of the point of intersection of
the Sumner line, we proceed to multiply OP by Fj to get the difference of longitude
AjO, and apply that difference to the known longitude of A l to find the longitude
of the point of intersection P; and also, as a check, to multiply OP by F 2 to get the
difference of longitude BA which, being applied to the longitude of B x , gives again
the longitude of the point of intersection, P.
164 THE SUMNER LINE.
The following is a summary of the successive steps to be taken in following this
method :
1. Make a rough sketch of the Sumner lines whose intersection is to be fixed in
latitude and longitude, classifying them under Case I or Case II.
2. Take from Table 47 the longitude factors Fj and F 2 , respectively, for the
Sumner lines.
3. If the given coordinates of the points on the two lines have not a common
latitude, reduce them to a common latitude by multiplying the difference between
the latitudes of the points on the two lines by the longitude factor of one of the
lines and applying the product to the longitude of the point on that line. The
sketch will show whether the difference of longitude is to be added or subtracted, and
the result will be the longitude of a point of this line on the common parallel of
latitude.
4. The difference between the longitudes of the points of the two Sumner lines,
on the common parallel, divided by the sum of the longitude factors (Fj-fF.,), will
give the difference of latitude between the point of intersection and the common
parallel, when the lines are classified under Case I; and the difference between the
longitudes of the points of the two Sumner lines, on the common parallel, divided by the
difference of the longitude factors (F x F 2 ), will give the difference of latitude between
the point of intersection and the common parallel, when the lines are classified under
Case II.
The sketch will show whether the intersection of the Sumner lines lies to the
northward or southward of the common parallel, and hence whether the difference
of latitude is to be added to or subtracted from the latitude of the common parallel.
5. Having found the difference of latitude between the point of intersection of
the Sumner lines and the common parallel, multiply this difference by the longitude
factor of each line and apply the products each to the longitude of its corresponding
line on the common parallel. The products are applied in opposite directions in
Case I, and both of them must lead to the same longitude for the point of intersection ;
and the products are applied in the same direction in Case II, and in this case also
both of them must lead to the same longitude for the point of intersection.
EXAMPLE: Find the intersection of the Sumner lines defined below by the latitude and longitude of
a single point on each and by the respective azimuths of the celestial bodies upon which the lines depend.
FIG. 58.
f 25 40 S 1
A j -Q^O 3^ ^ > Azimuth, at right angles to line, N. 51 E.
f OO on:/ Q ^
B 1 -no QQ/ c w ^Azimuth, at right angles to line, N. 72 W.
^ J-J-O oo O W J
From Table 47:
Longitude factor for line A=0.90=F!.
Longitude factor for line B=0.36=F 2 .
Reduce the given points to a common parallel of latitude by transferring
the point on line B to the latitude of the point on line A,
(25 40 S.-25 25 S.)XF 2 =15 X0.36= 5 .4 W.
115 33 .5 W.
115 38 .9 W.
Hence we have for the point on the line B at which the latitude is the same as the latitude of the point
on the line A,
{OCO Af)/ Q 1
115 38 9 W [Azimuth, at right angles to line, N. 72 W.
We now have two Sumner lines, under Case I, whose common latitude is 25 40 S. and whose longitudes
on the common parallel are:
115 38 .9 W.
115 31 .0 W.
7 / .9=Diff. Long, on common parallel.
79 79 79
p _|_-p = QQ\ 36 = ifi>6 == ^ 7 ^iff- kat. between intersection and common parallel.
THE SUMNER LINE.
165
Corrections in longitude:
6. 27XF 1= 6. 27X0. 90=5 . 64
6. 27XF 2 =6. 27X0. 36=2 . 26
Long. A
Diff. Long.
115 31 .OOW.
5.64W.
Intersection 115 36 .
Long. B 115 38 .90W.
Diff. Long. -2.26E.
115 36 .64 W.
Lat. common parallel 25 40 / .00 S.
Diff. Lat. 6 .27 N.
25 33 .738.
EXAMPLE: Find the intersection of the Sumner lines defined below:
f4Q <*(V N 1
A { 5 24 8 W j Azimutn > at ri 8 nt angles to line, N. 81 W.
T49 30 7 N 1
Bs c o~ Q w f Azimuth, at right angles to line, X. 31 W.
[ O /O .5 \V .J
A sketch of the lines shows their classification to be under Case II.
From Table 47:
Longitude factor for line A=0.24=F!.
Longitude factor for line B=2.57=F 2 .
Diff. Long, on common parallel=5 25 .85 24 .8=1 .0.
-F2- 57-0.
==Diff - Lat between
B
tion and common parallel.
Corrections in longitude:
FIG. 59.
0. 429XF a =0. 429X0. 24=0. 10.
0. 429XF 2 =0. 429X2. 57=1. 10.
Long. A
Diff. Long.
5 24 .8 W.
.IE.
Long. B
Diff. Long.
5 25 .8 W.
1 .1 E.
Lat. common parallel
Diff. Lat.
49 SO 7 .0 N.
.4 N.
Intersection 5 24 .7 W.
5 24 .7 W.
49 30 .4 N.
B
FIG. 60.
378. If the two geographical positions defining two Simmer lines have a
common longitude instead of a common latitude, as represented in figures 60 and 61,
their intersection may be found by means of the latitude factors
tabulated in Table 48, in a manner similar to the use of the lon
gitude factors in connection with the Sumner lines whose known
points have a common latitude. The latitude factors vary with
the latitude of the observer and the celestial body s azimuth at
right angles to the direction of the line, and express the change in
latitude due to a change of 1 in longitude along any given Sumner
line. So that the difference of longitude between any two points
of a line being multiplied by the latitude
factor will give the difference of latitude be
tween those points.
The latitude factors of two Sumner lines
whose intersection is to be found are usually
denoted by the letters i 1 and f 2 , and the
successive steps to be taken in finding the in
tersection are here summarized:
1. Make a rough sketch of the Sumner
lines whose intersection is to be fixed in latitude and longitude,
classifying them under Case I or Case II.
2. Take from Table 48 the latitude factors f x and f 2 ,
respectively, for the Sumner lines.
3. The difference between the latitudes of the points of
the two Sumner lines, in the common longitude, divided by
the sum of the latitude factors (fj + f 2 ), will give the difference
of longitude between the point of intersection and the common meridian when the
lines are classified under Case I; and the difference between the latitudes of the
FIG. 61.
166 THE SUMNER LINE.
points of the two Sumner lines, in the common longitude, divided by the difference
of the latitude factors (f x f 2 ), will give the difference of longitude between the point
of intersection and the common meridian when the lines are classified under Case II.
The sketch will show whether the intersection of the Sumner lines lies to the
eastward or westward of the common meridian, and hence whether the difference of
longitude is to be added to or subtracted from the common longitude.
4. Having found the difference of longitude between the point of intersection
of the Sumner lines and the common longitude, multiply this difference by the
latitude factor of each line and apply the products each to the latitude of its corre
sponding line on the common meridian. The products are applied in opposite
directions in Case I, and both of them must lead to the same latitude for the point of
intersection; and the products are applied in the same direction in Case II, and in
this case also both of them must lead to the same latitude for the point of intersection.
EXAMPLE: Find the intersection of the Sumner lines denned below:
A {yJ if go \v } Azim uth, at right angles to line, N. 57. 6 W.
B{^ J|| ^ ^ 1 Azimuth, at right angles to line, N. 77 W.
A sketch of the lines shows their classification to be under Case II.
From Table 48:
Latitude factor for line A=l. 23=f t .
Latitude factor for line B=3. 32=f t .
Diff. Lat. on common meridian =7 . 15.
7. 15 7. 15 7. 15
= - -= =3 . 42 Diff. Long, between intersection and common meridian.
f 2 -f t 3.32-1.23 2.09
Corrections in latitude:
3. 42X^=3. 42X1. 23= 4 . 20
3. 42Xf 2 =3. 42X3. 32=11 . 35
Lat. A 40 13 . 55 N. Lat. B 40 06 . 40 N. Long, on common me-
Diff. Lat. 4 . 20 N. Diff. Lat. 11 . 35 N. ridian 71 14 . 86 W.
Diff, Long. 3. 42 E.
Intersection 40 17 . 75 N. 40 17 . 75 N.
71 11 . 44 W.
379. When a Sumner line is defined by the latitudes and longitudes of two of
its points, the longitude factor for the line may be found by dividing the difference
between the longitudes of the two given points by the difference between their
latitudes; and the latitude factor, being the reciprocal of the longitude factor, may
be found by dividing the difference between the latitudes of the two given points by
their difference of longitude.
The method of finding the intersection of Sumner lines by longitude and lati
tude factors, described in articles 377 and 378, may, therefore, be applied as well
when the lines are defined by pairs of geographical positions as when they are defined
by the azimuth and one geographical position.
380. The modification of the methods for finding the intersection of two Sumner
lines, where there is a run between the observations from which they are deduced,
will be readily apparent. It is known that at the time of taking a sight the vessel
is at one of the points of the Sumner line, but which of the various points represents
her precise position must remain in doubt until further data are acquired. Suppose,
now, that after an observation, the vessel sails a given distance in a given direction;
it is clear that while her exact position is still undetermined it must be at one of the
series of points comprised in a line parallel to the Sumner line and at a distance and
direction therefrom corresponding to the course and distance made good; hence, if
THE SUMNEK LINE. 167
a second sight is then taken, the position of the vessel may be found from the inter
section of two lines one, the Sumner line given by the second observation, and the
other a line parallel to the first Sumner line but removed from it by the amount of
the intervening run.
Positions may be brought forward graphically on a chart by taking the course
from the compass rose with parallel rulers, and the distance by scale with dividers.
If one of the methods by computation be adopted, the point or points of the first
line are brought forward by the traverse tables, using middle latitude sailing. The
direction of a Sumner line as determined from the azimuth of the body always
remains the same, whatever shift may be made in the position of the point *by which
the line is further defined.
EXAMPLE: Taking the Sumner lines, which are denned in the first example under article 377. by the
latitude and longitude of a point of each and by the respective azimuths of the celestial bodies upon
which the lines depend, as follows:
A {ll5 31 W } Azimutn > at ri g ht angles to line, N. 51 E.
5 W } Azimutn > at right angles to line, N. 72 W.
33
and supposing the vessel from which the observations were taken that gave these lines to have
N. 54 E. (true) 35 miles in the interval between the sights, find the position of the vessel at the tim
run
time of
the second sight.
The point A ; in 25 4(X S. and 115 31 W., is first transferred to the point A , 35 miles N. 54 E.(true)
from A, by the method of Middle Latitude Sailing (article 177) by means of the Traverse Tables, thus:
From Table 2, course N. 54 E.; Dist., 35 miles; we find Diff. Lat. 20.6 N., Dep. 28.3 E. Therefore,
Lat. A 25 4(K S. Lat. A 25 4<X S.
Diff. Lat. 20 .6 N. Lat. A 25 19 .4 S.
Lat. A 25 19 .4 S. 2)50 59 .4
Middle Lat. 25 29 .7
From Table 2, Middle Lat, (course), 25, Dep. (Lat.), 28.3 E., we find Diff. Long. (Dist,), 31.3 E.
Therefore,
Longitude A. 115 31 W.
Diff. Long. 31 .3 E.
Longitude A , 114 59 .7 W.
The Sumner lines whose intersection is to be found are therefore defined as follows:
A/ {ll4 5<T *7 W } Azimutn at ri gnt an les to the line > N - 51 E -
B L^ I! 5 |; JAzimuth, at right angles to the line, N. 72 W.
From Table 47:
Longitude factor for line A / =0.90=F 1
Longitude factor for line B =0.36=F 2
Reduce the given points to a common parallel of latitude by transferring the point on line B to the
latitude of the point on line A ,
(25 19M S.-25 25 S.)XF 2 =-5.6X0.36= 2 .0 E.
115 33 .5 W.
115 31 .5 W.
Hence we have for the point on the line B at which the latitude is the same as the latitude of the point
on the line A 7 ,
^A 25 19 .4 S.
B \115 31.5W.
168 THE SUMNEK LINE.
We now have two Sumner lines, A and B , under Case I, whose common latitude is 25 19 . 4 S. , and whose
longitudes on the common parallel are 114 59 . 7 and 115 31 . 5. Hence, the difference of longitude on
the common parallel is
115 31 .5 W.
114 W.I W.
31 .8=Diff. Long, on common parallel.
O1 Q O1 Q ^18
-=^==25. 2=Diff. Lat. between intersection and common parallel.
25.2XF 1 =25.2X0.90=22.7
25.2XF 2 =25.2X0.36= 9.1
Corrections in longitude:
Long. A x 11459 / .7W. Long. W 115 31 r .5W. Lat. common par. 25 19 X .4 S.
Diff. Long. 22 .7 W. DifE. Long. 9.1 E. Diff. Lat. 25 .2 N.
Intersection 115 22.4W. 115 22.4 24 54 .2 S.
CHAPTER XVI.
THE PEAOTICE OF NAVIGATION AT SEA,
381. Having set forth in previous chapters the methods of working dead
reckoning and of solving problems to find the latitude, longitude, chronometer
correction, and azimuth from astronomical observations, it will be the aim of the
present chapter to describe the conditions which govern the choice and employment
of the various problems, together with certain considerations by which the navigator
may be guided hi his practical work at sea.
382. DEPARTURE AND DEAD RECKONING. On beginning a voyage, a good
departure must be taken while landmarks are still in view and favorably located for
the purpose; this becomes the origin of the dead reckoning, which, with frequent
new departures from positions by observation, is kept up to the completion of the
voyage, thus enabling the mariner to know, with a fair degree of accuracy, the posi
tion of his vessel at any instant.
At the moment of taking the departure, the reading of the patent log (which
should have been put over at least long enough previously to be regularly running)
must be recorded, and thereafter at the time of taking each sight and at every other
time when a position is required for any purpose, the Tog reading must also be noted.
It is likewise well to read the log each hour, for general information as to the speed
of the vessel as well as to observe that it is in proper running order and that the
rotator has not been fouled by seaweed or by refuse thrown overboard from the ship.
It is a good plan to record the tune by ship s clock on each occasion that the log is
read, as a supplementary means of arriving at the distance will thus be available in
case of doubt. If a vessel does not use the patent log but estimates her speed by
the number of revolutions of the engines or the indications of the chip log, the
noting of the time becomes essential. A good sight is of no value unless one knows
the point in the ship s run at which it was taken, so that the position it gave may be
brought forward with accuracy to any later time.
383. GENERAL DESCRIPTION OF THE DAY S WORK. The routine of a day s
work at sea consists in working the dead reckoning, an a. m. time sight and azimuth
taken when the sun is in its most favorable position for the purpose, a meridian alti
tude of the sun (or, when clouds interfere at noon, a sight for latitude as near the
meridian as possible), and a p. m. time sight and azimuth. This represents the
minimum of work, and it may be amplified as circumstances render expedient; but
no part of it should ever be omitted unless cloudy weather renders its performance
impossible.
384. MORNING SIGHTS. The morning time sight and azimuth should be
observed, if possible, when the sun is on the prime vertical. As the body bears
east at that tune, the resulting Sumner line is due north and south, and the longitude
will thus be obtained without an accurate knowledge of the latitude. Another
reason for^ so choosing the time is that near this point of the sun s apparent path
the body is changing most slowly in azimuth, and an error in noting the time will
have the minimum effect in its computed bearing. The time when the sun will be
on the prime vertical that is, when its azimuth is 90 may be found from the
azimuth tables or the azimuth diagram. Speaking generally, during half the year
the sun $ does not rise until after having crossed the prime vertical, and is therefore
never visible on a bearing of east. In this case it is best to take the observation as
soon as it has risen above the altitude of uncertain atmospheric effects between 10
and 15.
A series of several altitudes should be taken, partly^ because the mean is more
accurate than a single sight, and partly because an error in the reading of the watch
or sextant may easily occur when there is no repetition. If the sextant is set in
advance of the altitude on even five or ten minute divisions of the arc, and the time
169
170 THE PEACTICE OF NAVIGATION AT SEA.
marked at contacts, the method will be found to possess various advantages. As
the sight is being taken the patent log should be read and ship s time recorded. It
is well, too, to make a practice of noting the index correction of the sextant each time
that the sextant is used. The bearing of the sun by compass should immediately
afterward be observed, and the heading by compass noted, as also the time (by the
same watch as was used for the sight) .
Before working out the sight, the dead reckoning is brought up to the time of
observation, and the latitude thus found used as the approximate latitude at sight.
It is strongly recommended that every sight be worked for a Sumner line, either by
assuming two latitudes, or by using one latitude and the azimuth, or yet more
advantageously by the method of Saint Hilaire.
The compass error is next obtained. From the time sight the navigator learns
that his watch is a certain amount fast or slow of L. A. T., and he need only apply
this correction to the watch time of azimuth to obtain the L. A. T. at which it was
observed; then he ascertains the sun s true bearing from the azimuth tables or
azimuth diagram, compares it with the compass bearing, and obtains the compass
error; he should subtract the variation by chart and note if the remainder, the devia
tion, agrees with that given in his deviation table; but in working the next dead
reckoning, if the ship s course does not change, the total compass error thus found
may be used without separating it into its component parts. It should be increased
or decreased, however, as the ship proceeds, by the amount of any change of the
variation that the chart may show.
385. If there is any fear of the weather being cloudy at noon, the navigator
should take the precaution, when the sun has changed about 30 in azimuth, to observe
a second altitude and to record the appropriate data for another sight, though this
need not actually be worked unless the meridian observation is lost. If it is required
it may be worked for either a time sight or $ $" sight, or by the Saint Hilaire
method, according to circumstances, and a second Sumner line thus obtained, whose
intersection with earlier Sumner line, brought forward for the run in the interval
between the sights, will give the ship s position.
386. NOON SIGHTS. Between 11 and 11.30 o clock (allowing for gain or loss
of time due to the day s run) the ship s clocks should be set for the L. A. T. of the
prospective noon position. The noon longitude may be closely estimated from the
morning sight and the probable run. The navigator should also set his own watch for
that time, to the nearest minute, and note exactly the number of seconds that it is
in error. He may now compute the constant (art. 325, Chap. XII) for the meridian
altitude. The daily winding of the chronometer is a most important feature of the
day s routine, and may well be performed at this hour. At a convenient time before
noon, the observations for meridian altitude are commenced and continued until the
watch shows L. A. noon, at which time the meridian altitude is measured and the
latitude deduced.
If the weather is cloudy and there is doubt of the sun being visible on the meridian
an altitude may be taken at any time within a few minutes of noon, the time noted,
and the interval from L. A. noon found from the known error of the watch. It is
then the work of less than a minute to take out the a from Table 26, the at 2 from
Table 27, and apply the reduction to the observed altitude to obtain the meridian
altitude. Indeed, the method is so simple that it may be practiced every day and
several values of the meridian altitude thus obtained, instead of only one.
387. It now becomes necessary to find the longitude at noon. This may be
done graphically by a chart or bv computation. The former plan needs no explana
tion. There are a number of variations in the methods of computation, one of which
will be given as a type.
By the ship s run, work back the noon latitude to the latitude at a. m. time sight.
If the Sumner line was found from two assumed latitudes which differed + m minutes,
while the corresponding longitudes differed ri minutes, then 1 difference of latitude
A 1 )
causes minutes difference of longitude. If the true latitude at sight is#min-
ffb
utes from one of the assumed latitudes, thena: X is the corresponding difference of
longitude. If the Sumner line was found from one assumed latitude and an azimuth,
Z, the longitude factor of the line may be found from Table 47 ; and this multiplied
THE PRACTICE OF NAVIGATION AT SEA. 171
by the difference between the true and assumed latitude will give the correction to
be applied to the computed longitude corresponding to the assumed latitude.
Having thus the longitude at sight, the longitude at noon is worked forward for the
run. If the sights show a considerable current it should be allowed for, both in
working back the latitude and in bringing up the longitude for the run between the
sight and noon.
EXAMPLE: Suppose that an a. m. time sight, taken when the sun s azimuth was S. 39 48 E., has
given a longitude of 30 31 W. when solved with a dead-reckoning latitude of 50 54 N. Suppose that
when the noon latitude is worked back to the time of the a. m. sight, by means of the vessel s run, the
true latitude at that time was found to be 50 58 N. The longitude was thus computed with a latitude
that was 4 too much to the southward. Find the corresponding error in longitude, and the longitude
at the time of sight.
down in connection with the Explanation of Table 47, the correction in longitude must, in this case,
be applied to the eastward.
Hence we have-
Longitude computed with D. R. Lat., 50 54 N 30 31 W.
Correction in long, due to change of 4 in latitude to the northward 7. 6 E.
True longitude at the time of sight 30 23. 4 W.
388. CURRENT AND RUN. The current may be found by comparing the noon
positions as obtained by observation and by dead reckoning, and the day s run is
calculated from the difference between the day s noon position bv observation and
that of the preceding day. To "current" is usually attributed all discrepancies
between the dead reckoning and observations; but it is evident that this is not
entirely due to motion of the waters, as it includes errors due to faulty steering,
improper allowance for the compass error, and inaccurate estimate of tie vessel s
speed through the water.
The noon position by observation becomes the departure for the dead reckoning
that follows.
389. AFTERNOON SIGHTS. The p. m. time sight and azimuth is similar to the
morning observation.
390. SUMNER LINES. By performing the work that has just been described a
good position is obtained at noon each day, which, in a slow-moving vessel with
plenty of sea room, may be considered sufficient; but conditions are such at times as
to render it almost imperatively necessary that a more frequent determination of the
latitude and longitude be made. If the vessel is near the land or in the vicinity of
off-lying dangers, if she is running a great circle course requiring frequent changes,
if she is making deep-sea soundings, S she has just come through a period of fo^gy
or cloudy weather, or if the indications are that she is about to enter upon such a
period, or if she is running at high speed, it is obviously inexpedient to await the
coming of the next noon for a fix. The responsibilities resting upon the navigator
require that he shall earlier find his ship s position; and, generally speaking, the
greater the speed made by the vessel the more absolute is this requirement.
The key to all such determinations will lie in the Sumner line, and a clear under
standing of the properties of such a line will greatlv facilitate the solutions. The
mariner must keep in mind two facts: First, that a single observation of a heavenly
body can never, by itself, give the paint occupied by an observer on the earth s
surface; and second, that whenever any celestial body is visible, together with
enough of the horizon to permit the measuring of its altitude, an observer may
thereby determine a line which passes through his own position on the earth s surface
in a direction at right angles to the bearing of the body.
It may readily be seen that if two Sumner lines are determined the observer s
position must be at their intersection, and that that intersection will be most clearly
marked when the angle between the lines equals 90; hence, if two heavenly bodies
are in sight at the same time the position may be found from the intersection of their
Sumner lines, the angle of intersection being equal to the horizontal angle between
the bodies. If only one body is in sight, as is generally the case when the sun is
shining, one line of position may be gotten from an altitude taken at one time, and a
second line from another altitude taken when it has changed some 30 in^ azimuth
usually, a couple of hours later. Bringing forward the first line for the intervening
run, the intersection may be found.
172 THE PEACTICE OF NAVIGATION AT SEA.
With the general principles of the Sumner line clearly before him, the navigator
will find no difficulty in making the choice of available bodies. If about to take a
star sight, and sky and horizon are equally good in all quarters, two bodies should
be taken whose azimuths differ as nearly as possible by 90. If one body can be taken
on or near the meridian, its bearing being practically^ north or south, the resulting
Sumner line will be east and west that is, it may be said that whatever the longitude
(within its known limits) the latitude will be the same; the other sight may then
be worked as a time sight with this single latitude, and time will thus be saved. The
same is true if Polaris is observed, and it is a very convenient practice to take an
altitude of that star at dawn and obtain a latitude for working the a. in. time sight
of the sun. A similar case arises when a body is^ observed on the prime vertical,
its Sumner line then runs north and south and coincides with a meridian; if the other
body is favorably located for a q> <p" sight, it may be worked with a single longitude
and the latitude thus found directly.
If it is not possible to obtain two lines and thus exactly locate the ship, the
indications of a single line may be of great value to the navigator. A Sumner line
and a terrestrial bearing will give the ship s position by their intersection in the same
manner as two lines of position or two bearings; or the position of the ship on a line
may be shown with more or less accuracy by a sounding or a series of soundings.
If the body be observed when it bears in a direction at right angles to the trend of a
neighboring shore line, the resulting line will be parallel with the coast and thus
show the mariner his distance from the land, which may be of great importance even
if his exact position on the line remains in doubt. If the bearing be parallel to the
coast line, then the Sumner line will point toward shore; the value -of a line that leads
to the point that the vessel is trying to pick up is amply demonstrated by the
experience of Captain Sumner that led to the discovery of the method. (Art. 362,
Chap. XV.)
For especially accurate work three Sumner lines may be taken, varying in
azimuth about 120; if they do not intersect in a point, the most probable position
of the ship is at the center of the triangle that they form.
If two pairs of lines be determined, each pair based upon observation of two
bodies bearing in nearly opposite directions and at about the same altitude, the
mean position that results from the intersection of the four lines will be as nearly
as possible free from those errors of the instrument, of refraction, and of the observer,
which can not otherwise be eliminated. This is fully explained in article 449,
Chapter XVII.
391. USE OF STARS, PLANETS, AND MOON. It may be judged that the
employment in navigation of other heavenly bodies than the sun is considered of
the utmost importance, and mariners are urged to familiarize themselves with the
methods by which observations of stars, planets, and the moon may be utilized to
reveal to them the position of their vessels at frequent intervals throughout the
twenty-four hours.
It should be remembered, however, that in order to be of value these observations
must be accurate; and to measure an accurate altitude of the body above the horizon
it is required not only that the body be visible but also that the horizon be distinctly
in view. Care should therefore be taken to make the observations, if possible, at
the time when the horizon is plainest that is, during morning and evening twilight.
It may be urgently required to get a position during hours of darkness, and a dim
horizon line may sometimes be seen and an observation taken, using the star telescope
of the sextant; if the moon is shining, its light will be a material aid; but results
obtained from such sights should be regarded as questionable and used with caution.
Altitudes measured, however, just before sunrise and just after sunset are open to
no such criticism; a fairly well-practiced observer who takes a series of sights at
such a time, setting the sextant for equal intervals of altitude, will find the regularity
of the corresponding time intervals such as to assure him of accuracy.
392. IDENTIFICATION OF UNKNOWN BODIES. On account of the very great
value to be derived from the use of stars and planets in navigation, it is strongly
recommended that all navigators familiarize themselves with the names and positions
of those fixed stars whose magnitude renders possible their employment for obser
vations, and also with the general characteristics magnitude and color of the
three planets (Venus, Jupiter, and Mars) which are most frequently used. A study
THE PRACTICE OF NAVIGATION AT SEA. 173
of the different portions of the heavens, with the aid of any of the numerous charts
and books which bear upon the subject, will enable the navigator to recognize the
more important constellations and single stars by their situation with relation to
each other and to the pole and the equator.
It may occur, however, that occasion will arise for observing a body whose name
is not known, either because it has not been learned, or because the surrounding
stars by which it is usually identified are obscured by clouds or rendered invisible
by moonlight or daylight. In such a case the observer may estimate the hour angle
and decimation (the hour angle applied to local sidereal time giving the right
ascension), and the star or planet may thus be recognized from a chart or from an
inspection of the Nautical Almanac. This rough method will generally suffice when
the body is the only one of its magnitude within an extensive region of the heavens;
but cases often arise where a much closer approximation is necessary, and more
exact data are required for identification.
393. If in doubt as to the name of the body at the time of taking the sight, it
should be made an invariable rule to observe its bearing by compass, whence the
true azimuth may be approximately deduced by applying the compass error.
Star Identification Tables giving simultaneous values of the declination and
hour angle, corresponding to the values of the latitude, altitude, and azimuth ranging
from to 88 in latitude and altitude and from to 180 in azimuth, are published
by the Hydrographic ^ Office for the convenience of navigators. In the absence of
these Star Identification Tables, the following method affords a means of identi
fication:
sin d = sin L sin 7i + cos L cos Ti cos Z (1 )
sin t = sin Z cos Ji sec d (2)
Having computed the value of d, the declination, from (1), noting carefully the
sign of cosine Z, the value of t, the hour angle, is computed from (2) . In the catalogues
and lists giving the names and magnitudes of the stars, they are tabulated by their
declinations and right ascensions because these coordinates are independent of
diurnal rotation, and, this being so, it becomes necessary, on finding the hour angle
from (2), to convert it into right ascension; and then, with the values of the declina
tion and right ascension thus found, to scan the list of stars and find the name of
that one whose catalogued coordinates best agree with these values. The stars that
are bright enough to be observed with nautical instruments are so far apart in the
firmament that the identification will be complete if the computation be but roughly
made. The possibility that the observed body may be a planet must always be kept
in mind in scanning the star table or chart.
EXAMPLE : At sea, February 26, 1916, L. M. T. 6h 20m p. m. Weather overcast and cloudy. Observed
the altitude of an unknown star through a break in the clouds to be 31 3(X (true), bearing 285 (true).
What is the name of the star? Ship s position, by D. R., latitude 35 2(K N., longitude 60 W.
L 35 2(X log sin 9. 762 log cos 9. 912
h 31 3(X log sin 9. 718 log cos 9. 931 log cos 9. 931
Z 285 00 log cos 9. 413 log sin 9. 985
A 0.302 log... 9.480
B 0.180 log... 9.256
A-f B = 0.302 + 0.180 = 482 = nat sin d . . d = 28 49 / .. . log sec 10. 057
t=K. A.=70=4h 40m log sin 9.973
Then converting the hour angle into right ascension, as follows:
L. M. T. 6 h 20 m
R. A. M. S. 22 20
corr. for G. M. T. +2
L. S. T. 4 42
H. A. 4 40
R. A. 02
174 THE PRACTICE OF NAVIGATION AT SEA.
394. VALUE OF THE MOON IN OBSERVATIONS . Next to the sun, the most con
spicuous body in the heavens is the moon, and it may therefore frequently be
employed by the mariner with advantage. Owing to its nearness to the earth and
the rapidity with which it changes right ascension and declination, the various cor
rections entailed render observations of this body somewhat longer to work out,
with consequent increased chances of error; and errors in certain parts of the work
will have more serious results than with other bodies^ the navigator will therefore
usually pass the moon by if a choice of celestial bodies is offered for a determination
of position; but so many occasions present themselves when there is no available
substitute for the moon that the extra time and care necessary to devote to it are
well repaid. During hours of daylight it is often clearly visible, and its line of
position may cut with that of the sun at a favorable angle, giving a good fix from
two observations taken at the same time, when the only other method of finding
the position would be to take two sights of the sun separated by a time interval in
which an imperfect allowance for the true run intervening would affect the accuracy
of the result, or a clouding-over of the heavens would prevent any definite result
whatever being reached; and during the night, the gleam upon the water directly
below the moon may define the horizon and give opportunity for an altitude of that
body when it is impossible to take an observation of any other. It has been the
purpose of this work to point out the features of the various sights wherein the
practice with the moon differs from that of the sun, stars, or planets; care and
intelligent consideration will render these quite clear.
Besides its availability for determining Sumner lines of position, which it shares
with other bodies, the moon affords a means for ascertaining the Greenwich mean
tune independently of the chronometer, thus rendering it possible to deduce the
longitude and chronometer error. This is accomplished by the method of lunar
distances. 1 If the Greenwich time given by an observation of lunar distance could
be relied upon for accuracy, the method would be a great boon to the navigator;
but this is not the case. The most practiced observer can not be sure of obtaining
results as close as modern navigation demands, and the errors to which the method
is subject are larger than the errors that may be expected in the chronometer, even
when the instrument is only a moderately good one and its rate is carried forward
from a long voyage. The method is not, therefore, recommended for use except
where the chronometer is disabled or where it is known to have acquired some
extraordinary error; and when lunar distances are resorted to care must be taken
to navigate with due allowance for possible inaccuracy of the results. In this con
nection it is appropriate to say that the best safeguard against the dire consequences
that may result from a disabled or unreliable chronometer is for every vessel to carry
two or, far better, three of those instruments, the advantages of which plan are
stated in article 265, Chapter VIII.
395. EMPLOYMENT OF BODIES DEPENDENT UPON THEIR POSITION. The prac
tical navigator will soon observe that there are certain conditions in which bodies
are especially well adapted for the finding of latitude, and others where the longitude
is obtained most readily.
Taking the sun for an example, when a vessel is on the equator and the declina
tion is zero, that body will rise due east of the observer and continue on the same
bearing until noon, when for an instant it will be directly overhead, with a true
altitude of 90, and will then change to a bearing of west, which it will maintain
until its setting. In such a case any observation taken throughout the day will
give a true north-and-south Sumner line, defining longitude perfectly, but giving no
determination of the latitude, excepting for a moment only when the body is on the
meridian. With the exception noted, all efforts to determine the latitude will fail.
The reduction to the meridian takes the form ^, becoming indeterminate, and in the
<f> $" sight the cosine of < will assume a value that corresponds alike to any angle
within certain wide limits the limits within which the circle of equal altitude has
practically a north-and-south direction. In conditions approximating to this we
may obtain a longitude position more easily than one for latitude, even within a few
minutes of noon.
1 The tables of lunar distances have been omitted from the American Ephemeris and Nautical Almanac after the volume for
THE PRACTICE OF NAVIGATION AT SEA. 175
As the latitude and declination separate, conditions become more favorable for
finding latitude and less so for longitude; the intermediate cases cover a wide range,
wherein longitude may be well determined by observations three to five hours from
the meridian, and latitude by those within two hours of meridian passage. As
extreme conditions are approached the accuracy of longitude determinations con
tinues to decrease; at a point in 60 north latitude, when the sun is near the southern
solstice, its bearing differs only 39 from the meridian at rising; or, in other words,
even if observed at the most favorable position, the resulting Sumner line is such
that ! in latitude makes a difference of 1.3 miles of departure, or 2 . 6 of longitude,
and is far better for a latitude determination than for longitude. And in higher
latitudes still this condition is even more marked.
Having grasped these general facts, the navigator must adapt his time for
taking sights to the circumstances that prevail, and when the sun does not serve
for an accurate determination of either latitude or longitude the ability to utilize
the stars, planets, and moon as a substitute will be of the greatest advantage.
396. USE OF VARIOUS SIGHTS. Except when employing the method of Saint
Hilaire (Chapter XV), the navigator may sometimes be in doubt as to the best
method of working a sight. Xo rigorous rules can be laid down, and experience
alone must be his guide. In a general way it may be well, when the body is nearer
to the prime vertical than to the meridian, to work it for longitude, assuming lati
tude, and using the time sight; and when nearer the meridian to work it for latitude,
assuming longitude, by the < <f>* method. The time sight is more generally used
than the other, it has wider limits of accurate application and is probably a little
quicker; but as the meridian is approached and the hour angle decreases small
errors in the terms make large ones in the results. The <f> </>" or latitude method
should not ordinarily be employed beyond three hours from the meridian, and then
only when the body is within 45 of azimuth from the meridian and has a declina
tion of at least 3 Q ; with an hour angle of 6 h (90) or a declination of the trigono
metric functions assume such form that the method is not available; nor does it
give definite results when the azimuth is 90 or thereabouts.
When the body is close enough to the meridian for the method of reduction to
the mericlian to be applicable, that method is to be preferred because of its quickness
and facility. It should be noted, however, that, though close enough to employ
the reduction, it may not be sufficiently correct to assume that the body bears due
north or south, and the sight should be worked with two longitudes, or the Sumner
line determined by the azimuth, unless the bearing nearly coincides with the direc
tion of the meridian.
397. WORKING TO SECONDS AND ACCURACY OF DETERMINATIONS. The beginner
who seeks counsel from the more experienced in matters pertaining to navigation will
find that he receives conflicting advice as to whether it is more expedient to carry
out the terms to seconds of arc, or to disregard seconds and work with the nearest
whole minute.
It is a well-recognized fact that exact results are not attainable in navigation at
sea; the chronometer error, sextant error, error of refraction, and error of observa
tion are all uncertain; it is impossible to make absolutely correct allowance for them,
and the uncertainty increases if the position is obtained by two observations taken
at different times, in which case an exactly correct allowance for the intervening
run of the ship is an essential to the correctness of the determination. Xo navigator
should ever assume that his position is not liable to be in error to some extent, the
precise amount depending upon various factors, such as the age of the chronometer
rate^the quality of the various instruments, the reliability of the observer, and the
conditions at the time the sight was taken; perhaps a fair allowance for this possible
error, under favorable circumstances, will be 2 miles; therefore, instead of plotting
a position upon the chart, and proceeding with absolute confidence in the belief that
the ship s position is on the exact point, one may describe, around the point as a
center, a circle whose radius is 2 miles if we accept that as the value of the possible
error and shape the future courses with the knowledge that the ship s position may
be anywhere within the circle.
It is on account of this recognized inexactness of the determination of position
that some navigators assume that the odd seconds may be neglected in dealing with
176 THE PEACTICE OF NAVIGATION AT SEA.
the different terms of a sight ; the average possible error due to this course is probably
about one minute, though under certain conditions it may be considerably more. It
is possible that, in a particular case, the error thus introduced through one term
would be offset by that from others, and the result would be the same as if the
seconds had been taken into account; but that does not affect the general fact that
the neglect of seconds as a regular thing renders any determination liable to be in
error about one minute. Those that omit the seconds argue, however, that since, in
the nature of things, any sight may be in error two minutes, it is immaterial if we
introduce an additional possibility of error of one minute, because the new error is
as liable to decrease the old one as to increase it; but the fallacy of the argument
will be apparent when we return to the circle drawn around our plotted point... The
eccentricity of the sextant may exactly offset the improper allowance for refraction,
and the mistake in the chronometer error may offset the observer s personal error,
but unless we know that such is the case which we never can we nave no justi
fication for doing otherwise than assume that the ship may be any place within the
2-mile circle. If, now, we increase the possible error by 1 mile, our radius of uncer
tainty must be increased to 3 miles, and the diameter of the circle, representing the
range of uncertainty in any given direction, is thereby increased from 4 to 6 miles.
It is deemed to be the duty of the navigator to put forth every effort to obtain
the most probable position of the ship, which requires that he shall eliminate possible
errors as completely as it lies within his power to do. By- neglecting seconds he
introduces a source of error that might with small trouble be avoided. This becomes
of still more importance since modern instruments and modern methods constantly
tend to decrease the probability of error in the observation, and to place it within
the power of the navigator to determine his ship s position with greater accuracy.
398. There is a more exact way of denning the area of the ship s possible position
than that of describing a circle around the most probable point, as mentioned in the
preceding article, and that is to draw a line on each side of each of the Sumner lines
by which the position is defined, and at a uniform distance therefrom equal to the
possible error that the navigator believes it most reasonable to assume under existing
conditions; the parallelogram formed by these four auxiliary lines marks the limit
to be assigned for the ship s position; this method takes account of the errors due
to poor intersections, and warns the navigator of the direction in which his position
is least clearly fixed and in which he must therefore make extra allowance for the
uncertainty of his determination.
It must be remembered in this connection that no position can ever be obtained,
when out of sight of the land, except from the intersection of two Sumner lines,
whether or not the lines are actually plotted; thus, a meridian altitude gives a Sumner
line that extends due east and west, and a sight on the prime vertical a line that
extends north and south, though it may not have been considered necessary to work
the former with two longitudes or the latter with two latitudes.
399. THE WORK BOOK AND FORMS FOR SIGHTS. The navigation work book,
or sight book, being the official record of all that pertains to the navigation of the
ship when not running by bearings of the land, should be neatly and legibly kept,
so that it will be intelligible not only to the person who performed the work, but
also to any other who may have reason to refer to it.
Each day s work should be begun on a new page, the date set forth clearly at
the top, and preferably, also, a brief statement of the voyage upon which the ship is
engaged. It is a good plan to have the -dead reckoning begin the space allotted for
the day, and then have the sights follow in the order in which taken. The page
should be large enough to permit the whole of any one sight to be contained thereon
without the necessity of carrying it forward to a second page. No work should be
commenced at the bottom of a page if there is not room to complete it. Every
operation pertaining to the working of the sights should appear in the book, and all
irrelevant matter should be excluded.
It is well to observe a systematic form of work for each sight, always writing
the different terms in the same position on the page; this practice will conduce to
rapidity and lessen the chances of error. In order to facilitate the adoption of such
a method, there are appended to this work (Appendix II) a series of forms that are
recommended for dead reckoning, and for the various sights of the sun, stars,
THE PRACTICE OF NAVIGATION AT SEA. 177
planets, and moon, respectively. For beginners, these are deemed of especial
importance, and it is recommended that, until perfect familiarity with the dif
ferent sights is acquired, the first step in working out an observation be to
write down a copy of the appropriate blank form, indicating the proper sign of appli
cation of each quantity (for which the notes will be a guide), and not to put in any
figures until the scheme has been completely outlined; then the remainder of the
work will consist in writing down the various quantities in their proper places and
performing the operations indicated.
The navigator may make up his work book by having printed forms of the
various sights which can be placed in a loose-leaf binder when they have been filled
in with his computations. Instead of printed forms on separate sheets, he may
employ rubber stamps of the various forms of sights which he may stamp in his
work book or on loose leaves.
THE SPECIFIC STEPS FOB CARRYING OUT THE DAY S WORK.
400. The day s work as described herein is so laid out that the true position
at noon is known some few minutes before noon, as, when cruising in company,
naval vessels have to make their noon position report by signal at exactly 12 o clock.
When cruising singly the noon position need not be known until after 12 o clock,
but it is advisable to do a day s work always in one way, and, therefore, the plan of
getting the correct noon position before noon will be followed.
401 THE TIME TO TAKE AN A. M. OBSEKVATION. The navigator of a vessel
cruising may, by dead reckoning or by plotting on a chart, predict the approximate
position of me snip the following morning, and from that position may easily determine
the best time to observe the sun (or other body) for longitude. Having determined
his approximate 8 a. m. position, he takes from the Nautical Almanac the declination
of the sun for Greenwich noon of that day. With the latitude of the 8 a. m. position
and declination for the day, he enters tne Azimuth Tables and takes out tne local
apparent time when the sun will bear 90. By getting the error of his watch on local
apparent time for the approximate 8 a. 1 m. longitude, he may easily find the watch
tune when the sun will bear 90, which is the tune he should take his sight. Suppose
on the evening of July 18, 1916, a navigator finds that at 8 a. m. the next day he will
be in approximate Lat. 35 12 N., Long. 65 15 W., and wishes to find at what
time ly Ms watch the sun will be on the prune vertical. He compares his watch
with the chronometer, of which he knows the correction, and which is, we will say,
slow l m 10 s on G. M. T., and finds that when the chronometer reads, say ll h 59 m 30 s ,
the watch reads 7 h 15 m 12 s . He then does the following work:
He takes from the Nautical Almanac the declination and the equation of time
for Greenwich mean noon on July 19 and finds Dec. = 20 52 N.;. Eq. t. 6 m 04 8 ,
subtractive from mean time.
With Lat. 35.2 N., Dec. 21.0 N., enter the Azimuth Tables, and find, for a
bearing of 90, the L. A. T. is about 8 h 10 m .
Write down the reading of the chronometer face at comparison ll h 59 m 30 s
Apply the chronometer correction + 1 10
G. M. T. of the time of comparison 12 00 40
Apply equation of time 6 04
Greenwich apparent time of comparison 11 54 36
For Long. 65 15 W., X=4 h 21 m 00 s . Apply X 4 21 00
At time of comparison the L. A. T. at the 8 a. m. position was 7 33 36
At time of comparison the watch time was 7 15 12
Error of watch on L. A. T. of 8 a. m. position 18 24 slow.
L. A. T. when sun is on prime vertical 8 10
Watch time to take a. m. observation 7 51 36
The observation should therefore be taken when the watch face reads about 7-52,
which will bring the sun very close to the prime vertical.
When the latitude and decimation are of different names the sun crosses the
prune vertical before rising. In that case, the observation is taken as soon as the
61828 16 12
178 THE PRACTICE OF NAVIGATION AT SEA.
sun is sufficiently high to be unaffected by any peculiar condition of the atmosphere,
usually about an hour after sunrise. The L. A. T. of sunrise and sunset is given at
the bottom of the page in the Azimuth Tables. Suppose in the above example the
approximate 8 a. m. latitude was 35.2 S. instead of 35.2 N. Entering the tables
with Lat. and Dec. of different names, we find the time of sunrise is about 7 a. m.
The observation should therefore be taken at about 8 a. m. L. A. T., the watch time
of which can be found in the same way as explained above.
In a similar manner Azimuth Tables may be used to find the best time to take
p. m. observations for longitude.
402. THE MORNING WORK OF THE NAVIGATOR. The navigator, having deter
mined the time at which he will take his morning observation, is called sufficiently
early to be ready for work about 15 minutes before the time chosen.
The first thing the navigator does is to check up his time. To save the trouble
of going below to compare the watch with the standard chronometer each time that
an observation is taken, most navigators keep the hack chronometer in the chart
house and use it for comparisons during the day. It is necessary to check the hack
with the standard chronometer each day to make sure of its error on G. M. T. and
rate. This comparison is made the first thing in the morning, the date, the error
on G. M. T., and the rate of the hack being written on a slip of paper that is placed
in the hack case. The hack is then taken to the chart house and is used for the
day s work. As hack chronometers frequently have hi<jh daily rates, an additional
correction sometimes has to be made for the rate when observations have been taken
some hours after the comparison. The hack is sometimes used for marking the time
of observation, and. when so used, the G. M. T. is at once obtained by applying the
hack error.
Having checked up the hacu chronometer, the navigator then prepares his
sextant and takes it, with his watch and notebook, to the place from which he takes
his observations. At about the time he has selected for his purpose, he observes
altitudes of the sun, which, with the corresponding watch times are noted in his note
book. The patent log is read while the observations are being taken and the reading
is entered in the notebook. The navigator then goes to the standard compass and
gets a bearing of the sun, which with the watch time of the bearing and the compass
eading of the ship is entered in the notebook. Either just before or just after
observing the altitude of the sun with the sextant, the index correction should be
found and entered in the notebook. The navigator next compares his watch with
the hack chronometer and gets the C-W, which is also entered in the notebook.
From the log book he gets tne courses and distances run from the last "fix" and
enters them in his notebook. This completes the data for his morning s work.
The computations are then made in the navigator s work book. The first step
is to work up the dead reckoning from the last "fix" to the time of sight. It may
be well here to call the attention of the student to the fact that for "distance run"
the propellers frequently are a more accurate gauge than the patent log which some-
tunes gets foul. In a smooth sea the distance by revolutions is usually very accurate,
especially if the effect of the condition of the bottom as to fouling is loiown. In
heavy weather the patent log is a better gauge as the effects of the wind and sea on
the speed of the ship are hard to determine. But for distance run both the patent
log and revolutions should be considered, and, if there is a discrepancy between
them, it should be investigated and the more accurate distance should be used.
Having brought the dead reckoning up to the time of sight, the latitude so found
is taken as the base of the computation of the longitude by observation. It is
assumed that the student is familiar with the various methods of getting a line of
position from an observation. Any one of the various methods gives the same line
and the choice of method is naturally the choice of the individual.
Having obtained the line of position, the longitude factor is next found, as
explained in article 387. The longitude factor is used twice, first to find the longitude
by observation corresponding to the D. R. latitude, and again after the noon latitude is
determined, to find the true noon longitude. As soon as the longitude factor has been
obtained, the longitude by observation corresponding to the D. R. latitude is found,
and it is this point on* the line of position that is used for the rest of the work to noon.
This point, corrected for run, is also the point adopted as the 8 a. m. position, and
THE PRACTICE OF NAVIGATION AT SEA. 179
as by using it future steps are simplified, it is advisable always to work from this
point. Of course, any other point on the line can be moved up, and the final result
will be the same, but the computation will be a little more complicated.
Having obtained the position at time of sight (D. R. Lat., Long, by obs.) and
the longitude factor, the navigator next proceeds to get the compass error. The
work he has already performed in getting the line of position gives nun certain data
that will shorten his work in finding the compass error. If the sight has been worked
out as a Simmer line the navigator, by taking the L. A. T. found by his computation
and correcting it for the difference between the watch times of his observation for
altitude and observation for azimuth, may obtain at once the L. A. T. of the time
at which he took the sun s azimuth. With this L. A. T., and the Lat. and Dec. used
in working out his sight, he may at once find from the Azimuth Tables the true
bearing of -the sun and get the compass error. If the line of position has been
obtained by one of the tangent methods, the navigator has, in his computation, deter
mined the true bearing of the sun at the tune of sight. All he has to do to get the
true azimuth for compass error is to correct this bearing for the change in azimuth
due to the difference in time between his observation for altitude and his observation
for azimuth. This correction is easily found from the Azimuth Tables by inspection.
This completes the morning work when the amount of work each day is a
minimum. When very accurate positions are required at other times than at
noon, as for instance, when a vessel is scouting, when in dangerous waters,
moving at high speed, or when making a landfall, other lines of position are
worked out, and the ship s position found on each line by moving the next preceding
line up to it for run. For instance, lines obtained from morning twilight sights of
the moon, stars, or planets, may be run up to the 8 a. m. line, the 8 a. m. line may
be run up to one taken at 9.30 or 10, or later, and so on. When getting the position
by the intersection of lines moved up for run, it is usual to perform the work on the
plotting charts supplied for this particular purpose. These charts are Mercator
projections covering each 5 of latitude from to 60. The parallels are numbered
for every degree of latitude, and the navigator selects the chart covering the latitude
in which he is working. The meridians on these charts, not being numbered, the
navigator is left free to mark them with the longitudes through which he is working.
The charts are of large scale, and, being on heavy paper, may be used over and over,
lines on these being drawn in lightly and erased when no longer required.
Intersections of lines of position may be computed, as explained in Chap. XV,
when there are no charts at hand suitable for plotting the lines graphically. Special
plotting sheets prepared by the United States Hydrographic Office are supplied to
vessels of the Navy.
403. THE WORK BETWEEN 11 A. M. AND NOON. Two important steps, not
usually fully explained in the text books, must be studied. These are: First, to
determine me exact run from the time of the a. m. sight to local apparent noon;
second, to set the watches and clocks to the local apparent tune of the place the ship
will be at local apparent noon.
If the ship has been making westing, the watches and clocks will be ahead
of the local apparent time of the noon position and will have to be set back by the
amount of the change in longitude. As the change of time is made between 11 a. m.
and noon, it will be seen that the elapsed time between the tune of the a. m. sight
and the new watch time of noon wiQ be more than the watch face shows by the
amount the watch has been set back, and this difference must be allowed for in
computing the run to noon. In the same way, if the ship has been making east
ing, the clocks and watches will have to be set ahead and the elapsed time between
the time of the a. m. sight and the new watch time of noon will be less than the watch
face shows by the amount the watch has been set ahead, and must be allowed for in
computing me run to noon. It must be remembered that this time can not be
computed exactly, but it can be approximated very closely in this way. Suppose a
ship has been steaming on course 66 true, and the navigator finds from his a. m.
observation taken at watch time, 8 h 00 m 03 8 .5, that the L. A. T. for the position,
Lat. by D. R. 38 03 .2 N., Long, by obs. 72 50 26" W., is 8 h 17 m 23 S .9. He sees
at once that at 8 a. m. his watch is already slow 17 m 20 S .4 on L. A. T. Now, if he
180 THE PEACTICE OF NAVIGATION AT SEA.
continues on this course 66 true, at a speed of 11.7 knots per hour, the watch will
be still slower at noon. He therefore turns to the Traverse Tables and finds that
on that course and at a speed of 11.7 knots the ship will each hour go 10.69 miles to
the eastward, which, in Lat. 38, makes a change of longitude of 13 . 6 each hour.
Now, from time of sight to 11 a. m. the change of longitude will be 3X13 .6 = 40 .8
of longitude, which is equal to a further loss 01 2 m 43 s . 2 of time; but the watch was
already slow 17 m 20 S .4, so that at 11 a. m. the watch will be slow 20 m 03 8 .6, and
the time to noon will be l h (20 m 04 s ), the difference due to change in longitude in
39 m 56 s (l h - 20 m 04 s ) . Now39 m 56 s = 0.66 h and the change of longitude = 0.66 X 13 .6 =
9 .0 of long. = 36 s . of time. Hence the total amount the time will be changed will be :
Change to time of a. m. sight 17 m 20 s . 4
Change between a. m. sight and 11 a. m 2 43 . 2
Change between 11 a. m. and L. A. noon 36 .
Total change 20 39.6
and the run to noon will be four hrs. minus this change = 3 h 39 m 20 S .4 = 3.66 hrs. The
distance run to noon will be 3.66 h X ll kts .7 = 42 kts .8.
The navigator can now run the a. m. point, determined by dead reckoning lati
tude and longitude by observation, up to noon, and, after that he is ready to set
his watch and clocks to the time of the coming local apparent noon position.
404. If the body observed for the a. m. sight was on or near the prime vertical,
the longitude found from it would be correct for the time of observation, since an error
in latitude makes no change in the longitude. This longitude when compared with
the longitude by dead reckoning at the time of sight will show if there has been an
easterly or westerly set of the current, and the amount of it. If a current is found
and allowed for, for the time of the run from time of sight to noon, the noon longitude
can be found very accurately. If the heavenly body used for the a. m. observation
was not near the prime vertical, the exact easterly- or westerly set can not be deter
mined; but a close approximation to it can generally be made by comparing the.
longitude found by observation with the D. R. longitude, and the current so found
should be allowed for in running the a. m. point up to noon. The error will be
small and will give results sufficiently accurate for ordinary work. Having allowed
for easterly or westerly current and having run the a. m. position point by observa
tion up to noon, the navigator can then set his watch to local apparent time of the
noon position, and his watch can be used to set the deck clocks. A convenient way
to set the watch is as follows : Having looked at the hack face and found what it
reads, say 4 h 09 m 50 s , let it be determined to set the watch to the correct local
apparent time of the noon position when the hack face reads 4 h 15 m 00 s .
Write down reading of hack face at time watch is to be set 4 h 15 m 00 s
Apply the hack correction (in this case hack is 5 m 38 s fast on G. M. T. ) ( - ) 5 38
This gives G. M. T. at which watch is to be set to L. A. T 4 09 22
Apply equation of time corrected for longitude of noon position (+)H 33.8
This gives G. A. T. of time watch is to be set 4 20 55.8
Now apply longitude for noon position (in this case) 4 48 23
Watch face should read 11 32 32.8
The watch is now to be set so that, at 4 h 15 m 00 s by hack, the watch face will show
as near ll h 32 m 33 s as possible. It will be found, since the second hand of a watch
can not be set, that the watch can not be set to the exact reading. By care, however,
the watch can be set so that it will be 30 seconds or less fast or slow on the desired
time. The number of seconds the watch is fast or slow on L. A. T. should be noted
in the work book, as it will be a help in taking near-noon sights to get the correct
L. A. T. at once from the reading of the watch face instead of comparing the watch
again with the chronometer. The watch being set as nearly as possible to the
correct L. A. T. and the error being recorded, the deck clocks are set ; and the navi
gator then proceeds to work up his constants for his near-noon observations for
latitude, and completes all his forms and fills them out as far as possible before
taking the observations.
THE PRACTICE OF NAVIGATION AT SEA. 181*
405. Now suppose the navigator wishes to take his observations at 15, 10, and
5 minutes before local apparent noon and desires to get constants for these times to
which he can apply his sextant altitudes and at once get his correct noon latitude.
To find the watch times at which he should take these observations, he must know
the error of his watch on local apparent time of the place of observation. He knows
the error of his watch on the L. A. T. of the noon position (in this case we will sup-
Eose the watch is IS 8 fast). He knows that on course 66 true, speed 11.7 knots, in
at. 38, that in 1 hour he changes longitude 13 .6. Therefore 15 minutes before
noon the ship will be 3 .4 of longitude west of where it will be at noon = 13 8 .6 of time.
Hence the observation 15 minutes before noon should be taken at watch time
ll h 45 m 00 8 + 18 8 ( = amount watch is fast on L. A. T. of noon position) + 13 8 .6
(= amount watch is fast on L. A. T. of place of first near-noon observation) = ll h
45 m 31 S .6. Similarly the observation taken 10 m before noon should be taken at
watch time ll h 50 m 00 8 -f 18 8 + 9M ( = amount watch is fast on L. A. T. of place of
second observation) = ll h 50 m 27M. The observation taken 5 minutes before noon
should be taken at watch time ll h 55 m OO s -H8 s + 4 8 .5 ( = amount watch is fast on
L. A. T. of place of third observation) = ll h 55 m 22*.5. A meridian altitude would
of course be taken at watch time 12 h 00 m 18 s .
Having obtained the watch times of the observations, the navigator next works
out the constants. These constants are obtained in the same way as meridian
altitude constants but to each are applied two corrections to the meridian altitude
constant. These are:
(1) at 2 or the correction to be applied to an observed altitude near noon to make
it a meridian altitude.
(2) JL or the difference in latitude for the run from the time of observation
to noon.
In working out the constant, the method of obtaining a meridian altitude con
stant is followed and the two corrections mentioned above are applied to it. In
getting a meridian altitude constant, one has first to ascertain the approximate
altitude. If the student will in every case plot his elements roughly on the plane
of the meridian, putting O, the observer, at the center, a horizontal line through the
O with the right end marked S for south, and the left end N for north, to represent
the horizon, and draw a vertical line upward from O (marking its intersection with
the circle Z) to represent the zenith, he can by inspection write out his formulae and
see exactly how to apply all corrections. A few minutes 7 study will make this method
clear and will fully repay the very slight mental effort required to master it.
Now suppose L is the latitude of the noon position and L the latitude of the
point from which the near-noon observation was taken. Then L = L JL where
JL is the change in latitude from the tune of observation to noon.
Suppose, by inspection of the figure we have drawn, we see that for a meridian
altitude,
L = 90-cZ-obs. alt. corr. to alt.
Now when the observed altitude is taken before noon the correction at 2 has to
be applied to it to bring it to what the meridian altitude would be. Therefore, for
an altitude taken before noon,
L =90-<Z-(obs. alt. + aZ 2 ) corr. to alt.
= 90 - d - obs. alt. - at 2 corr.
L =90-d-obs. alt,-a^con\JL.
= K-obs. alt,
or K = 90 - d - at 2 corr. ^/L.
Having the watch time at which the near-noon observation is taken and K corre
sponding to it, it is only necessary to apply the observed altitude to its proper K
to get the correct noon latitude. Having the correct noon latitude, find by how
many minutes it differs from the D. K. noon latitude and multiply this difference
by the longitude factor to get the correction to be applied to the 8.00 a. m. longitude
by observation run up to noon, in order to get the correct noon longitude. This
182 THE PRACTICE OF NAVIGATION AT SEA.
part of the work is done roughly on deck in the navigator s note book as soon as the
altitude is taken. To facilitate this work the navigator writes his data in his note
book in the following form, filling the blank spaces alter getting his altitude :
For watch time ll h 45 m 30 ll h 50 m 26 s ll h 55 m 22- 12 h 00 m 18-
K 84 54 44 84 59 03 85 01 29 85 02 02
Obs. Alt.
Noon Lat. by Obs.
Mean
Noon Lat. by D. R. 38 20 35"
DL
Long, factor (Tab. 47) . 65
Corr. in Long.
Noon Long, by a. m. Obs. 72 05 44"
True longitude at noon
406. Having obtained the correct noon position in the above manner, the
navigator completes his work in his work book and plots the ship s position on the
chart. Having the correct noon position, he compares it with his previous noon
position (or point of departure) and gets the true course and distance made good.
Having the position by dead reckoning and by observation, he gets the set and
drift of the current. He then computes the total distance gone since leaving port
and the distance yet to go to his destination. Blank forms xor the noon report are
arranged for the following data:
(1) Lat. by observation.
(2) Long, by observation.
(3) Lat. by D. R.
(4) Long, by D. R.
(5) Current: Set and Drift.
(6) Course made good.
(7) Distance made good since noon.
(8) Distance made good since departure.
(9) Distance to destination.
If the course sailed is a rhumb line, and the ship is practically on the line laid
out as the track, no change of course is necessary. If the ship is decidedly off the
rhumb line course as laid out, or is sailing on a great circle track that requires a
change in compass course, the new course is laid out as soon as the true noon position
is obtained. This completes the navigator s work to noon.
407. THE AFTERNOON WORK OF THE NAVIGATOR. In the afternoon the navi
gator must take an observation for longitude. He selects a time when the sun is
as near as possible to the prime vertical, which time is determined in the same way
as explained for the a. m. observation. He runs his true noon position up to the
time of his p. m. observation, making an allowance for any evident current that was
found at noon. He then gets a position point on a line of position determined from
his observation. This point is run up to 8 p. m. by dead reckoning, which position
is plotted on the chart and completes the minimum navigation work for any day.
When particularly accurate positions are required, especially at 8 p. m., the
navigator takes an additional observation of the sun, or of some other heavenly body
at twilight, and gets the intersection of two lines of position. Or he may get a line
for longitude and a line for latitude by an altitude of Polaris or another star. In
this way the navigator may, at either morning or evening twilight, get a very accurate
fix; and this is done frequently. In fact, fixes obtained from observations of two
heavenly bodies taken at about the same time are the most accurate fixes that can be
obtained at sea, as the intersection of the two lines of position give a position point
that is correct at the time, no matter what the current is. Careful navigators will
therefore take such observations and the student should prepare himself to do so.
The methods of using position points obtained in this way are exactly the same as
the methods of using the points already explained.
THE PRACTICE OF NAVIGATION AT SEA. 183
The following example will give a good idea of the minimum day s work for the
navigator at sea. The form laid out is one that can always be followed. The cosine-
haversine formula is used for getting the lines of position, but any other method may
be substituted for it.
EXAMPLE: On October 4, 1916, the U. S. S. Delaware left Hampton Roads for
Lisbon. From the Chesapeake Capes the great circle course was followed. The
distance to Lisbon by great circle course is 3,120 miles. It is 25 miles from Hampton
Roads to the point from which the departure was taken. At 5 p. m., with Cape Henry
Light bearing 301 (mag.), dist. 8.3 miles, took departure, set course 74 (p. s. c.)
(Var. 5 W., Dev. 3 W.), and put over patent log, reading 0. (The point of de
parture is Lat. 36 51 59" N., Long. 75 51 03" W.)
The next morning by comparison with the standard, the hack chronometer was
found to be 5 m 38 8 fast on G. M. T. and gaining l a .5 daily. At about 8 a. m., patent log,
reading 175.0, the navigator took an a. m. observation for longitude: W. T. 8 h 00 m
03 8 .5; obs. alt. 22 55 10"; I. C. + l 50"; ht. of eye 40 ft. The navigator then
observed an azimuth of the sun as follows: W. T. 8 h 02 m 29 s ; bearing of sun p. s. c.
125 30 ; ship s head 74. He then compared his watch with the hack as follows:
hack face l h 13 m 00 s ; watch face 8 h 10 m 11 s .
Perform the a. m. part of the day s work.
The ship continues on same course at same speed (11.7 knots). When the hack
face reads 4* 15 m 00 s , at what time should the watch be set to be on local apparent
time at the noon position ?
If the watch was set 18 seconds fast on local apparent time at the noon position,
work out constants for observations for latitude to be taken 15, 10, and 5 minutes
before noon and at noon. Prepare all forms for the noon work.
The observed altitudes near noon were as follows: 15 minutes before, 46 12 30*;
10 min. before, 46 16 50"; 5 min. before, 46 19 20". The noon alt. was 46 19 40".
The patent log read 217.5 at noon.
Complete the day s work for noon.
At noon the course was changed to 86 (p. s. c.), Var. 10 W., Dev. 4 W.
Steamed until 4p. m. on this course, when at W. T. 4 h 00 m 12", obs. alt. of sun
18 32 40"; C-W, 4 h 40 m 56 8 ; I. C., +1 50"; ht, of eye, 40 ft.; patent log reading,
264.3.
Find position of ship at 4 p. m. by observation.
The course and speed remaining unchanged, find the 8 p. m. position.
184
THE PKACTICE Otf NAVIGATION AT SEA
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CHAPTER XVII.
MAEINE SURVEYING.
4:08. DEFINITIONS. Surveying is the art of making such field observations and
measurements as are necessary to determine positions, areas, elevations, and move
ments on the surface of the earth, giving its characteristic features, such as, on land,
the position of prominent objects, heights, and depressions, and on water, the depth,
nature of bottom, position of shoals, and velocity of currents.
Topographic Surveying relates to the land, and Hydrograpjiic Surveying to the
water; and both are underlaid by Trigonometrical Surveying which, when it is carried
on with high precision over such large areas as to contribute to form a basis for
determining the size and shape of the earth, becomes a department of Geodetic
Surveying.
It is not deemed appropriate to include in this work a complete treatise on
marine surveying. The scope of this chapter will be to set forth such general infor
mation regarcling the principles of surveying and the instruments therein employed
as will give the navigator an intelligent understanding of the subject sufficient to
enable him to comprehend the methods by which marine charts are made, and, if
occasion should arise, to conduct a survey with such accuracy as the instruments
ordinarily at hand on shipboard permit. For a more detailed discussion of marine
surveying, the student is referred to the various publications which treat the subject
exhaustively.
INSTRUMENTS EMPLOYED IN MARINE SURVEYING.
409. THE THEODOLITE AND TRANSIT. The Theodolite (fig. 62) is an instrument
for the accurate measurement of horizontal and vertical angles. While these instru
ments vary in detail as to methods of construction, the essential principles are always
identical.
A telescope carrying crosshairs in the common focus of the object glass and
eyepiece is so mounted as to have motion about two axes at right angles to one
another; graduated circles and verniers are provided by which angular motion in
azimuth and (usually) in altitude may be measured; and the instrument is capable
of such adjustment by levels that the planes of motion about the respective axes
will correspond exactly with the horizontal and the vertical.
The telescope is carried in appropriate supports upon a horizontal plate which
has, immovably attached to it, one or more verniers, and which revolves just over a
graduated circle that is marked upon the periphery of a second horizontal plate, a
means of measuring the motion of the upper plate relative to the lower one being
thus provided. Thumb screws are fittecf by which the upper plate may be clamped
to the lower, and (excepting in some simpler forms of me instrument) others by
which the lower plate may be made immovable in azimuth, or allowed free motion,
at will; all clamping arrangements include slow-motion tangent screws for finer
control.
A vertical graduated circle, or arc, with a vernier, clamps, and tangent screws,
is fitted to most theodolites, for the measurement of the angular motion of the tele
scope in altitude.
The theodolite usually carries a magnetic needle, with a graduated circle and
vernier for compass bearings. The instrument is mounted upon a tripod, and levels
and leveling screws afford a means of bringing the instrument to a truly horizontal
position.
189
190
MARINE SURVEYING.
The Transit used in surveying is a modified form of the theodolite, and is
generally employed where less accuracy is required; it takes its name from the f act-
that the telescope may be turned completely about its horizontal axis, or transited,
without removal from its supports.
410. The line of collimation of a telescope is an imaginary line passing through
the optical center of the object glass in a direction at right angles to that of its axis of
rotation. This is also called the axis of collimation. The line of sight is an imaginary
line passing through the
optical center of tne ob
ject glass and the point
of intersection of the
cross hairs.
A theodolite or
transit, before it can be
used for the accurate
measurement of angles,
must be in adjustment
in the following re
spects: (a) The vertical
axes of revolution of
the upper and lower
horizontal plates must
be coincident; (&) the
axis must be vertical
and the plates horizon
tal when the bubbles of
the levels are in their
central positions; (c)
the vertical cross hair
must be perpendicular
to the horizontal axis of
the telescope; (d) the
line of collimation must
coincide with the line of
sight; (e) the horizon
tal axis of the telescope
must be perpendicular
to the vertical axis of
the instrument; (f) the
bubble of the telescope
level must stand at the
middle of its scale, and
the vertical circle must
read zero, when the line
of collimation is hori
zontal.
The last-named
condition may be disre-
FIG. 62. garded if vertical angles
are not to be measured.
The instrument being in adjustment, to observe angles it should be set
up, leveled, and focused. This involves placing the tripod so that a plumb bob
from the center of the instrument shall hang directly over the spot at which the
measurement is to be made. The legs of the tripod should be firmly placed in such
manner that the height shall be convenient for the observer and the instrument
shall be nearly level. Then the horizontal plates are brought to a true level by
means of the leveling screws and bubbles. The telescope should next be focused
by moving the object glass and eyepiece in such manner that the object sighted
MARINE SURVEYING. 191
and the cross hairs may be plainly seen and that the object will not appear to have
motion relatively to the cross hairs as the eye is moved to the right or left of the
eyepiece. This last condition insures the cross hairs being at the common focus of
the eyepiece and objective.
To observe a horizontal angle with a theodolite or transit, clamp the upper
plate to the lower at zero, leaving the lower plate undamped; swing the telescope
so that its vertical cross hair bisects one of the objects, and clamp the lower plate;
unclamp the upper plate and bring the telescope to bisect the other object, and the
reading of the vernier on the scale will give the required angle. (Tne final nice
motion by which the cross hair is brought exactly upon a point is always given by
the tangent screw.)
In taking a round of angles, this operation is repeated successively upon each
object to be observed about the horizon, the upper piate always being swung, while
the lower is kept svhere set upon the first object, or origin. The result will give the
angular distance of each object from the origin, and, If the observations have been
accurately made, upon finally sighting back to the origin, the reading should be zero.
To repeat an angle, having made the first measurement of it in the usual way,
unclamp the lower circle and swing back the telescope until it again points to the
first object, and clamp it; then unclamp the upper circle, swing to the second object,
and clamp. The scale reading should now be double that of the first angle. Repeat
as often as the importance of the angle requires, and the accepted value will be the
final reading divided by the number of measurements. An angles of the main
triangulation, and others of importance in the survey, are repeated.
Defects in adjustment of the instrument may be eliminated by taking one
series of angles with the telescope direct and another with the telescope reversed. To
reverse the telescope, revolve it about its horizontal axis through 180, then swing
it about its vertical axis through 180 in other words, invert it.
Vertical angles are measured on the same principle as that described for hori
zontal ones.
The process of setting up the instrument at a station and observing the angles
between the various objects that are visible is called occupying the station.
412. THE PLANE TABLE. This is an instrument by which positions are plotted
in the field directly upon a working sheet. It consists (fig. 63) of a drawing board
mounted upon a tripod in such manner as to be capable of motion in azimuth, and
with facilities for being brought to a perfect level; in connection with it is employed
an alidade, consisting of a straightedge ruler, upon which is mounted a telescope
with cross hairs whose line of si<mt is exactly parallel to the vertical plane through
the edge of the rule. It is evident that if a sheet representing a chart be placed
upon such a board and turned so that the true meridians, as portrayed thereon, He
in the direction of the earth s meridian at that place, then all lines of bearings on
the chart will coincide with the corresponding lines on the earth s surface; from
which it follows that if the alidade be so placed that its rule passes through the spot
on the chart representing the position of the observer, while the telescope is directed
to some visible object, the position of that object on the chart lies somewhere upon
the line drawn along the edge of the rule. Upon this general principle depend the
various applications of the plane table.
The drawing board is usually made of several pieces of well-seasoned wood,
tongued and grooved together, with the gram running in different directions to
prevent warping; about its edge are several metal clips for securing the paper in
place. It is supported upon three strong brass arms, to which it is attached by
screws, thus permitting its removal at will. The arms are attached to a horizontal
plate which revolves upon a second horizontal plate lying immediately below it; a
clamp and tangent screw are fitted, by which the upper plate, and with it the draw
ing board, may oe secured to the lower plate, or may be given a fine motion in azimuth.
Three equidistant lugs of brass, grooved on the under side, project down from the
lower plate, resting on screws in the top of the tripod, by which the instrument is
leveled; when adjusted in this respect it is firmly clamped in position, and, as the
tripod is made unusually large, the adjustment is not easily deranged.
192
MARINE SURVEYING.
The alidade is a metal straightedge with a vertical column at its center, at the
top of which are the supports which carry the telescope; a vertical arc and vernier
are provided for measuring the motion of ^ the telescope ir\ altitude. The telescope
is usually so fitted that it may be revolved in azimuth through an arc of exactly 180,
for the purpose of adjusting the line of collimation. On top of the rule near its center
is the level sometimes replaced by two levels at right angles by means of which it
may be seen when the table is in a true horizontal position.
A magnetic needle mounted in a rectangular metal box, whose outer straight
edge is parallel to the zero line of a graduated scale over which the needle swings, is
provided for drawing the north-and-south line on the chart; this is called a declinatoire.
FIG. 63.
4:13. To be hi correct adjustment, a plane table must comply with the following
conditions:
(a) The fiducial edge of the rule must be perfectly straight. (6) The level must
have the bubble in its central position when the table is truly horizontal, (c) The
vertical cross hair must be perpendicular to the horizontal axis of the telescope.
(d\ The line of collimation must coincide with the line of sight, (e) The horizontal
axis of the telescope must be parallel to the plane of the table. (/) The vertical
circle should read zero when the line of collimation is horizontal.
&14:. The results derived from the use of the plane table, like all others dependent
upon graphic methods, must be regarded as less accurate than those deduced by
computation, and even less accurate than those derived from the careful plotting of
theodolite angles. Hence it is that, in a careful marine survey, this instrument
would be employed only for the topography and shore line.
For whatever purpose used, the plane table would not ordinarily be called into
requisition until the survey had so far progressed that a chart could be furnished the
observer showing certain stations whose positions were already established; with
this chart, the first step would be to occupy one of the determined points. The table
MARINE SURVEYING. 193
must be set up with the point on the chart directly over the center of the station ; it
must then be leveled and the telescope focused as described for the theodolite or
transit; and finally it must be oriented that is, so turned in azimuth that all lines of
the chart are parallel to similar lines of the earth s surface. To orient, unclamp the
table and swing it until the north-and-south line of the chart is approximately
parallel to that of the earth, one means of doing which is afforded by the declinatoire;
place the alidade so that the edge of the rule passes through the points on the chart
representing the station occupied and some second station which is clearly in view;
then, sighting through the telescope, perfect the adjustment of the table by swinging
it until the second station is exactly bisected by the vertical cross hair, the final slow
motion being obtained by clamping the table and working the tangent screw. If the
adjustment has been correctly made, the rule may be laid along the line joining the
station occupied and any other on the chart, and the telescope will point exactly to
that other station.
Being properly oriented, if the alidade be so placed that the edge of the rule pass
through the station occupied and the telescope point directly to some unknown
object whose position is to be determined, then a line drawn along the rule will
contain the point which represents the position of that object. If, now, the plane
table be set up at a second station, oriented for its new position, and a Hue be similarly
drawn from that station toward the one to be established, it will intersect the first
line in the required point. This is the method of determining positions by prosection.
Actually, the surveyor does not regard the point as well established until the inter
section is checked by a line from a third station.
In practical work, of course, each station is not occupied separately for the
determination of each point; the instrument is set up at a station, lines are drawn
to all required points in view, and each line is appropriately marked; then a second
station is occupied, and the operation is repeated, and so on, the various intersections
being marked as the work proceeds.
A second method of establishing positions is that of resection; in this the first
line is drawn from some known station, as in the preceding method, and the observer
next proceeds to the place whose position is required and occupies it ; the plane table
is there oriented by means of the line already drawn, placing the edge of the rule
along the line, sighting back toward the first station, and swinging the table until
that station is in the line of sight of the telescope; then choose some other established
station as nearly as possible at right angles to the direction of the first; place the
edge of the rule upon the plotted position of this station and swing the alidade (the
rule always being kept on the plotted point) until the object is bisected by the
telescope cross hairs; draw this fine, and its intersection with the first will give the
required point, the accuracy of which can be checked from some other plotted station.
A third method of locating a point is by means of a single bearing from a known
station, with the distance from the occupied station to the required one, the process
of plotting being self-evident.
A fourth method is given by occupying an undetermined position from which
three established stations are in view; the point occupied by the observer is then
plotted by an application of the "three-point problem."
415. It may be seen that where the greatest accuracy is not essential the plane
table may be employed for plotting all the points of a survey. In such a case it would
only be necessary to begin with the two base stations, plotted on the sheet on any
relative bearing whatsoever and at a distance apart equal to the length of the base
line (reduced to scale), as measured by the most accurate means available. The
work of plotting might even proceed before the base line had been measured, the
two stations being laid off at any convenient distance apart; when later the base
line was measured, the scale of the chart would be determined, being equal to the
distance on the chart between base stations divided by the length of the base line.
416. A plane table could be improvised on shipboard which would greatlv
facilitate the operation of any surveying work that a vessel not equipped with
instruments might be called upon to perform. A drawing board could be mounted
upon a tripod (as, for example, the tripod supplied for compass work on shore) in
such manner as to be capable of motion in azimuth ; it could be brought nearly to the
horizontal, if no better means offered, by moving the tripod legs, and this adjust-
61828- 16 13
194 MARINE SURVEYING.
ment could be proved by any small spirit level; sight vanes could be erected upon
an ordinary ruler to take the place of the alidade; in case there was difficulty in
observing any object with such an alidade, because of its altitude or for other reasons,
a horizontal angle might be observed with a sextant and plotted with a protractor.
By this means work could be done which, even if it should lack complete accuracy,
might be of great value.
417. THE TELEMETER AND STADIA. Any telescope fitted with a pair of hori
zontal cross hairs at the focus may be used as a telemeter, and when accompanied
by a graduated staff, called a stadia, affords a means of measuring distance (up
to certain limits) with a close degree of accuracy; the method consists in observing
the number of divisions of the scale subtended by the hairs when the stadia
is held perpendicular to the line of sight of the telescope, it being evident
that the closer the distance the fewer divisions will appear between them. The
f acility with which distances can be measured by this method makes it most important
that all telescopes of theodolites, transits, and plane tables be fitted as telemeters
and that stadia rods be provided for all surveying work.
Speaking approximately, it may be said that the number of divisions intercepted
between the cross hairs will vary directly as the distance of the stadia rod. This
would be exactly true if we looked at the object through an empty tube, directly
between the hairs. Since, however, the rays from the stadia are refracted by the
object glass before they are intercepted by the wires, the statement, to be absolutely
exact, must be slightly modified; but for practical surveying work it may be accepted
as given.
418. There are two methods of installing the telemeter cross hairs the first, in
which they are immovably secured in the telescope and always remain at the same dis
tance apart, and the second, in which the distance of the cross hairs is made variable,
being under the control of the observer. The former is generally regarded as the
preferable method, and when it is employed it is evident that the subtended height
of the stadia bears a constant ratio to the distance of the staff from the telescope.
It proves most convenient in practice to space the hairs so that this constant ratio
is some even multiple of 10, for facility in converting scale readings into distance;
it is also advantageous to mark the stadia in the unit of the chart scale and decimals
thereof; for example, if the ratio of stadia height to distance were 100, and the
stadia were marked in meters and decimals, a reading of 2.07 would at once be con
verted into a distance of 207 meters. Any units and any ratio may, however, be
employed, and for any given setting of cross hairs it is very easy to graduate a stadia,
by experiment, for any desired units; for example, if it is required to mark the
stadia in feet, set up and level the telescope, measure off a distance of exactly 100
feet from it, hold up an unmarked staff and mark upon it the points intersected by
the cross hairs; the interval between these marks will represent 100 feet of the
scale; divide this length into 100 parts, each of which will represent a distance of
one foot, and mark the whole staffon the same scale; then if the stadia be held up
at any distance, the cross hairs will intercept a number of divisions corresponding
to the number of feet of distance.
When the cross hairs are movable the ratio becomes variable, but the principle
of measuring remains the same namely, the distance of the staff from the telescope
is equal to the existing ratio multiplied by the distance intercepted on the scale.
4:19. The stadia is made of alight, narrow piece of wood and is usually hinged
for convenience in transporting. Ordinarily the background of the scale is painted
white, while ^the main divisions are marked in red, with minor divisions in black,
and geometrical figures are employed to facilitate the reading of fractional parts of
the scale. Devices are furnished by which the man holding the stadia may know
when it is vertical an essential condition for accuracy of measurements.
4:20. The use of the telemeter and stadia for measuring distances is limited to
the distance at which the scale divisions can be accurately read through the tele
scope. f For fairly close work and with the class of telescope usually supplied with
surveying instruments, 400 meters represents about the greatest distance at which
it can be employed. With this limitation, the character of the survey determines
the nature of its employment. In a careful survey its greatest use would be in
connection with the theodolite or plane table in putting in shore lines, contour lines,
MARINE SURVEYING. 195
and topography generally. In a survey where only approximate results are sought
it might afford the best means for the measurement of the base.
421. If the telemeter be applied to a theodolite, transit, or plane table which is
fitted with a graduated vertical arc or circle, it is possible to measure the distance to
the stadia not only in a horizontal but also in a vertical direction. In this case the
vertical angle must be observed as well as the stadia reading. Tables are computed
giving the solution of the triangles involved when the stadia rod is held vertical.
422. In making a survey with the ordinary resources of a ship, the principle of
the telemeter and stadia may be profitably employed, using a sextant and improvised
staff. In this case it is usual to have the stadia of some convenient fixed length
as, for example, 10 feet and of slight width and thickness; this is held at right
angles to the line of sight from the observer, who notes the angle subtended by the
total length; tables are prepared by which the distance corresponding to each angle
is given.
423. THE SEXTANT. This instrument is of the greatest value in hydrographic
surveying. It is fully described elsewhere in this work and its adjustment explained.
(Chap. VIII.)
Sextants are manufactured of a form especially adapted to surveying work;
they are smaller and lighter than those usually employed in astronomical observa
tions, but have a longer limb, by which angles may be measured up to 135; the
vernier is marked for quick reading and has no finer graduation than half minutes;
the telescope has a large field.
This instrument is principally employed in measuring the horizontal angles by
means of which soundings are plotted. It may, however, be put to various uses when
making an approximate survey, as has already been explained. It should be remem
bered, in measuring terrestrial angles with a sextant, that rigorous methods require
a reduction to the horizontal if either of the objects has material altitude above the
horizon.
424. THE LEVEL. This is an instrument for the accurate measure of differences
of elevation. It consists of a telescope, carried in a Y-shaped rest, which is mounted
upon a tripod and leveled in a manner similar to a theodolite; but it differs from that
instrument in that the telescope is not capable of motion about a horizontal axis
and in having no graduated circles for measurements of altitude and azimuth. The
principle of its use contemplates placing the line of collimation of the telescope in a
truly horizontal plane and keeping it so fixed.
425. It is principally employed in marine surveying to determine heights and
contour lines the latter being lines of equal elevation above the sea level and for
locating benchmarks for tidal observations. (Chap. XX.) In connection with it is
used a graduated staff called a leveling rod, carrying a conspicuous mark, adjustable
in height, called a target. To ascertain the difference of level between any two
points, set up the level with the telescope horizontal at some place between them;
let an assistant take the leveling rod to one of the points, and, while holding it on the
ground in a truly vertical position, move the target, under the direction of the
observer at the telescope, to a point where it is exactly bisected by the horizontal
cross hair; the height of the target on the staff that is, the height of the cross hair
above the level of the first point is then accurately read with a vernier; now,
without moving the level, shift the rod to the^second point and again adjust the
target and read it. It is evident that a comparison of the reading at the first posi
tion with that at the second will give the difference of height at the two points.
The difference that can be read from one location of the instrument is limited by
the length of the rod; but by making a sufficient number of shifts any difference
may be measured.
The work of the level may be performed equally well by a theodolite whose
telescope is adjusted to the true horizontal.
426. HELIOTROPE AND HELIOGRAPH. These are instruments sometimes
employed in surveying, by means of which the sun s rays may be reflected in any
given direction; the object of their use is to render conspicuous a_ station which is
to be observed at a distance and which would not otherwise be distinguishable.
The instruments vary widely in form of construction and, in the absence of those
made for the purpose, substitutes may easily be devised.
196
MARINE SURVEYING.
427. ASTRONOMICAL TRANSIT INSTRUMENTS. Various instruments are employed
for the astronomical determinations necessary in a marine survey. Among these are
the zenith telescope and portable transit. While differing in detail they consist essen
tially of a telescope mounted upon a horizontal axis that is placed truly in the prime
vertical, thus insuring the revolution of the line of collimation in the meridian; a
vertical graduated circle and vernier are supplied, affording a measure of altitude;
in the focus are a number of equidistant vertical cross hairs or lines; a small lamp
is so placed that its rays illuminate the cross hairs and render possible observations
at night. Latitude is obtained by observing the meridian altitude of stars; hour
angle (and thence longitude) by observing the times of their meridian transit, which
is taken from the mean of the times of passing all of the vertical cross hairs.
Excepting in surveys of a
most accurate nature, the astro
nomical determination of position
by the sextant and artificial hori
zon is regarded as satisfactory.
428. THE THREE -ARMED
PROTRACTOR, OR STATION
POINTER. This is an instrument
whereby positions are plotted
on the principle of the three-
point problem," of which an ex
planation is given in article 152,
Chapter IV. It consists (fig. 64)
of a graduated circle with three
arms pivoted at the center; each
arm has one edge that is a true
rule, the direction of which always
passes through the center of tne
circle. The middle arm is immov
ably fixed at the zero of the scale;
the right and left arms each re
volve about the center on their
own sides, and are provided with
verniers giving the angular dis
tance from the middle arm. The
protractor being set for the right
and left angles, it is so moved that
the three arms pass through the
respective stations, when the cen
ter marks the position of the ob
server. Center pieces of various
forms are provided, being cylin
drical plugs made to fit into a
socket at the pivot, and by em
ploying one or the other of them
FIG. G4. the true center may be pricked
with a needle, dotted with a pen
cil, or its position indicated by cross hairs. Adjustable arms are provided which
can be fitted to the ends of the ordinary arms when working with distant signals.
The most valuable use of the three-armed protractor is in plotting the positions
of soundings taken in boats, where sextant angles between signals are observed.
It may occur, however, that certain shore stations will be located by its use.
429. As this instrument is not made with both right and loft arms capable of
being set to small angles down to 0, the manufacturers make protractors with
either small right or small left angles. Surveying parties should be equipped with
both. In default of a three-armed protractor, a piece of tracing paper may be made
to answer its purpose. To use the tracing paper, draw a line, making a dot on it
to represent the center station, and with the center of an ordinary protractor on
MARINE SURVEYING.
197
FIG. 65.
the dot, lay off the two observed angles right and left of the line; then, laying this
on the plan, move it about till the three lines pass exactly through the three stations
observed. The dot from which they were laid off will be on the position of the observer,
and must be pricked lightly through or marked underneath in pencil.
430. THE BEAM COMPASS. This instrument (fig. 65) is employed in chart
drafting and performs the functions of compasses and dividers when the distance
that must be spanned is beyond the limits of those instruments in their ordinary
form. It consists of an angular bar of wood or metal upon which two instruments
termed beam heads are fitted in such a manner that the bar may slide easily; through
them. A clamping screw attached to one side of the beam head will fix it in any
part of its course along the beam. Upon
each head a socket is constructed to carry
a plain point, exchangeable for an ink or a
pencil point. To secure accuracy the
beam head placed at the end of the beam
has a fine adjustment, which moves the
point a short distance to correct any error
in the first rough setting of the instrument.
This adjustment generally
consists of a miBed-head
screw, which passes through
a nut fixed upon the end of
the beam head, which it car
ries with its motion.
431. PROPORTIONAL
DIVIDERS. These are prin
cipally employed for reduc
ing or enlarging drawings in
any given proportion. They
consist (fig. 66) of two narrow
flat pieces of metal called legs, which turn upon a pivot whose position
is movable in the direction of their length. The ends of both legs are
shaped into points like those of ordinary dividers. When the pivot is
fixed at the middle of the legs, any distance measured by the points
at one end is just equal to that measured by those at the other; for
any other location of the pivot, however, the distances thus measured
will not be equal, but with a given setting of the pivot any distance
measured by one end bears a fixed ratio to that measured by the other.
The path of travel of the pivot is graduated so that the ratio may be
given any desired value. Being adjusted in this respect, if a distance
is taken off a chart with the legs at one end of the instrument, then
those at the other end will show the same distance on the scale of a
chart enlarged or reduced in the proportion represented by the ratio
for which the pivot was set.
METHODS EMPLOYED IN A HYDROGRAPHIC SURVEY.
432. Before commencing a survey a general inspection of the field
is made; a base line is located and its extremities marked by signals;
certain other positions, known as main triangulation points, are selected
FIG. 66. and also marked with signals, being so chosen that, starting with the
base and proceeding thence from one to another of these points, a
series of well-conditioned triangles or quadrilaterals may cover the field of survey.
The base line is measured with the greatest degree of accuracy which the resources
of the survey render possible. Each extremity of the base line and each other main
triangulation point is occupied by an observer with a theodolite, who measures the
angles at each station between all the other stations which are in sight. ^ An astro
nomical determination is made of the latitude and longitude of some point of the
survey (frequently one of the extremities of the base) and of the true azimuth of
some known line (frequently the base line). Data are now at hand for the location,
upon the chart of the base line and main triangulation points.
198 MARINE SURVEYING.
If the survey is one of considerable extent, it is expedient to measure a check base
near the end of the triangulation. A comparison between the measured length of
this base and its length as computed through the chain of triangles will show the
degree of accuracy and afford a means of reconciling discrepancies. The position of
a second observation spot may be determined for a similar purpose.
The primary triangulation gives a skeleton of the field, but the points thus
determined are not usually close enough together to afford a basis for ail the detail
work that must be done. A second system of points is therefore selected and signals
erected thereon, and the position of these points is determined by a series of angles
from the main triangulation points and from one another. This is known as the
secondary triangulation. The points thus located are used in the plotting of the
topography and hydrography. It is not essential that their determination be as
accurate as that of main triangulation points.
The topography is put in, and includes the delineation of the features of the
land shore line, lighthouses, beacons, contour lines, peaks, buildings, and, in
short, everything that may be recognized by the navigator and utilized by him in
locating the ship s position.
The hydrographic work is taken up and the depth of water and character of
bottom determined as accurately as possible for the complete water area, especial
care being taken to develop all shoals and dangers to navigation and to locate all
aids to navigation, such as buoys, lightships, and beacons.
One or more tidal stations are established where observations are taken, con
tinually and at frequent intervals, of the height of the tide and direction and velocity
of the tidal and other currents, whence data are derived for the reduction of all sound
ings to the plane of reference and for the information about tides and currents which
is to appear upon the chart.
Observations are made to determine the magnetic variation and dip, and the
intensity of the earth s magnetic force.
433. The foregoing represent, in outline, the various steps that must be taken
in the accumulation of the data necessary for the construction of a complete hydro-
graphic chart. In the following paragraphs the details of the various operations will
be more f ully set forth.
The navigator who is called upon to conduct a marine survey without having
available the time, instruments, and general facilities necessary for the most thorough
performance of the work must exercise his discretion as to the modifications of method
that he will make, and call upon his ingenuity to adapt his means to the particular
work in hand.
434. THE BASE LINE. As the base line is the foundation for all distances on
the chart, the correctness of the results of the survey will depend largely upon the
degree of accuracy with which it is measured. The triangulation merely affords a
measure of the various distances as compared with the distances between the two
initial points from which it began; if that initial distance is 1,000 feet, we have cer
tain values for the. sides of the various triangles; if the same base line is 2,000 feet,
the value of each side becomes twice as great as it was before; with the same triangu
lation, therefore, distances vary directly with the length of the base line; it may
thus be seen that if an error exists in measurement which is only a small fraction
of the total length, the error will become much more material as the more distant
points of the survey are reached. In a base line 1,000 feet long, if a mistake of 10
feet be made all distances measured upon the chart will be in error 1 per cent, and
a point plotted by triangulation 10 miles from the observation spot (the point at
which plotting begins), would be out of its correct position one-tenth of a mile.
It is ^important that the base line should be as long as possible, consistent with
the distribution and distances between the surrounding objects which must be
depended upon as triangulation stations for its expansion. The position of the line
must be such as to afford favorably conditioned triangles and quadrilaterals with
adjoining main triangulation points, and its extremities must be visible from those
points and from each other. The character of the ground and the facility for meas
uring will of course form an important consideration in the choice.
435. In measuring a base by tape, chain, or similar means, a number of suc
cessive fleets are made with the measure, whatever its nature, the distance traversed
MARINE SURVEYING. 199
being appropriately marked after each fleet, while an observer, with a theodolite or
transit, insures the measurement being made accurately along the line.
436. The most careful measurements are made with a steel tape 300 feet long,
stretched along a series of supports at equal intervals along the base line, the points
of support being made exactly horizontal by a level. A good form of support is a
stake driven vertical with one side on the base line and a nail, for supporting the
tape, driven horizontally into the stake at the established level. The stakes falling
at the ends of tape lengths should be set slightly less than 300 feet apart, sawed on
at the established level, and have strips of zinc tacked on then- tops. The end of
each fleet is marked by a scratch mark cut in the strip of zinc at an even hundredth
of a foot-division on the tape, and the corresponding tape reading recorded. Tapes
for base-line measurement are usually subdivided to hundreclths of a foot for a
distance of 10 feet from each end of the tape. The tape is stretched to a uniform
tension by a spring balance. The temperature of the tape at each fleet should be
observed, and the mean temperature, for the entire measurement of the base deduce.
Tapes for base-line measurements are usually standardized lying flat, and at a
temperature of 62 Fahrenheit. To reduce the measured length of the base line
to the true length the f ollowing corrections to the measured length must be applied :
Temperature correction C t = + (<*T m - T ) L,
where a = coefficient of expansion.
T m = mean temperature at measurement.
T = standard temperature.
L = measured length.
Correction for sag C.= ~^C~w )
where L = measured length.
w = weight per inch of tape.
d = distance between supports in inches.
P = tension in pounds.
By this method of measurement the horizontal distance between the ends of
the base line may be readily found to within 1 part in 250,000, and by application
of superior apparatus, of several measures, and greater care hence, at an increased
cost the probable uncertainty may be reduced to 1 part in 500,000, but this degree
of accuracy would not be necessary except in very extended systems of triangulation.
437. A second method of base measurement is with the surveyor s chain.
This depends for accuracy upon the surface traversed being plane and level, a con
dition that is weh 1 fulfilled on a sandy beach, where the chain is nearly as accurate
as the tape and much more rapid. A surveyor s chain is usually 100 feet long; the
exact value of its length must be obtained by comparison with a standard, and a
correction applied for expansion or contraction due to temperature. The ends of
the fleets are marked by steel pins driven into the ground; the alignment is kept
by the theodolite.
438. Where neither chain nor tape is available substitutes may be improvised
from sounding wire taken from the deep-sea sounding machine, or failing this, from
well-stretched cod line.
Measurements made by the telemeter and stadia afford a close approxima
tion to the true result, and if these instruments are not at hand the sextant angle
of a rod of fixed length can be employed. The masthead height of the vessel may
be used in determining the length of base line on this principle, either by making
the ship itself mark one of the extremities and observing the masthead angle from
the other extremity, or by simultaneously observing the masthead angle from both
ends of a shore base, and also the three horizontal angles of the triangle formed by
the ship and the two base stations. The latter plan is far preferable where accuracy
is sought, as, if the angles are all taken by different observers at the same instant
(whicn can be marked by the hauling down of a flag), the error arising from the
motion of the ship about her anchor is eliminated, and, moreover, the data furnished
offers a double solution of the triangle and the mean may be taken as giving a closer
result.
200 MARINE SURVEYING.
439. A crude method of estimating distance is by means of the velocity of
sound, though this would never be used where close results are expected. Fire a gun
at one end of the distance and at the other note by the most accurate means available
the time between seeing the flash and hearing the report. Repeat several times in
each direction. The mean number of seconds and tenths of a second multiplied by
the velocity of sound per second at the temperature of observation (art. 314, Chap.
XI) gives the approximate distance.
440. When for any reason the existing conditions do not permit of a direct
measurement being made along the line between the two base stations, recourse
must be had to a broken base, that is, one in which the length of the base is obtained
by reduction from the measured length of two or more auxiliary lines. Necessity
for resorting to a broken base arises frequently when the two stations are situated
on a curving shore line and the straight line between them passes across water, or
where wooded or unfavorable country intervenes, or where a stream must be crossed.
The most common form of broken base is that in^which the auxiliary lines run from
each extremity of the base at an acute angle and intersect; in addition to measuring
each of these lines the angle formed by their intersection or else the angles formed
by them with the base line must be observed and the true length of the base deduced
by solution of the triangle. The form that is most frequently used where only a
short section of the base is incapable of measurement (as is the case where a deep
stream flows across) is that of an auxiliary right triangle whose base is the required
distance along the base line and altitude a distance measured along a line perpen
dicular thereto to some convenient point; by this measured distance and the angles
which are observed, the triangle is solved and the length of the unmeasured section
determined.
441. In a survey of considerable extent, where good means are at hand for the
correct determination of latitude and longitude, a base line actually measured upon
the earth may be dispensed with, and, instead of that, the positions of the two
stations which are most widely separated may be determined astronomically and
plotted; the triangulation is then plotted upon any assumed scale, and when it has
been brought up to connect the two stations the true value of the scale is ascertained.
This is called the method of an astronomical base.
442. SIGNALS. All points in the survey whose positions are to be located from
other stations, or from which other positions are to be located, must be marked by
signals of such character as will render them distinguishable at the distance from
wnich they are observed. The methods of constructing signals are of a wide variety.
A vessel regularly fitted out for surveying would carry scantlings, lumber, bolts,
nuts, nails, whitewash, and sheeting for the erection of signals ; however meager the
equipment, the whitewash and sheeting (or some substitute for sheeting, preferably
half of it white and half dark in color) should be provided, if possible, before begin
ning any surveying work. Regular tripod signals, which are quickly erected and
are visible, under favorable circumstances, for many miles, are almost invariably
employed to mark the main triangulation stations; among other advantages the
tripod form permits the occupation with the theodolite of the exact center of the
station, and avoids the necessity for the reduction which must otherwise be applied.
Signals on secondary stations take an innumerable variety of forms, the requirement
being only that they shall be seen throughout the area over which they are to be
made use of; a, whitewashed spot on a rock, a whitewashed trunk of a tree, a white
washed cairn of stones, a sheeting flag, a piece of sheeting wrapped about a bush,
or hung, with stones attached, over a cliff, or a whitewashed barrel or box filled with
rocks or earth and surmounted by a flag, suggest some of the secondary signals
that may be employed; sometimes objects are found that are sufficiently distinct in
themselves to be used as signals without further marking, as a cupola or tower, a
hut, a lone tree, or a bowlder; but it is seldom that an object is not rendered more
conspicuous by the flutter of a flag above it, or by the dead-white ray reflected from
a daub of whitewash.
For convenience, each signal is given some short name by which it is designated
in the records.
For the sake of economy in both time and labor, steel towers, such as are used
to support windmills, are being extensively employed by hydrographic parties for
MARINE SURVEYING. 201
surrey signals. They are very easily erected and dismounted, easily transported,
offer little resistance to gales of wind, and are more permanent and satisfactory than
signals of wood.
4:13. THE MAIN TEIAXGULATIOX. The points selected as stations for the main
trian oblation mark in outline -the whole area to be surveyed ; they are close enough
together to afford an accurate means of plotting all intermediate stations of the
secondary triangulation; and they are so placed with relation to one another that
the triangles or quadrilaterals derived from them are well conditioned. The points
are generally so chosen that small angles will be avoided. In order to fulfill the
other conditions, it frequently becomes necessary to carry forward the triangulation
by means of stations located on points a considerable distance inland, such as moun
tain peaks, which would not otherwise be regarded as properly within the limit* of
the survey.
Great care should be taken in observing all angles upon which the main triangu
lation is based; the best available instrument should be employed; angles taken
with a theodolite or transit should be repeated, and observed with telescope direct
and reversed, and the mean result taken; if the sextant is used, a number of separate
observations of each angle should be taken and averaged for the most probable
value. It must be remembered that while, in any other part of the work, an error
in an angle affects only the results in its immediate vicinity, an error in the main
triangulation goes forward through all the plotting that comes after it.
It occurs frequently that the. purposes of the survey are sufficiently well fulfilled
by a graphic plotting of the mam triangulation, but where more rigorous methods
prevail, tne results are obtained by calculation. The sum of the angles of each
triangle is taken, and if it does not exactly equal 180 the values are adjusted to
make them comply with this condition. In cases where the triangulation stations
form a series of quadrilaterals, the angles of each quadrilateral are adjusted so as to
form a perfect geometrical figure. Allowance is made for the curvature of the earth
where tne area of triangles is sufficiently large to render it expedient to do so. The
lengths of the various sides and the relative latitudes and longitudes of the several
stations are then computed. Each station may then be plotted in its latitude and
longitude on a polyconic projection, and a delineation of the triangulation system
may thus be obtained free from the accumulated errors of a graphic plotting.
" 444. THE SECONDARY TRIANGULATION. The points of the secondary triangu
lation are located, as far as possible, by angles from the main triangulation stations;
these angles, having less dependent upon them, need not be repeated. A graphic
plotting of these stations, without calculation, will suffice.
4:4:5. ASTRONOMICAL WORK. This comprises the determination of the correct
latitude and longitude of some point of the survey, and of the true direction of some
other point from the observation spot, thus furnishing an origin from which all posi
tions and all directions can be determined either graphically or by computation.
The methods of finding latitude, .longitude, and the true bearing of a terrestrial
object are fully set forth hi previous chapters. The feature that distinguishes such
work in surveying from that of determining the position of a ship at sea lies in the
greater care tnat is taken to eliminate possible errors.
The results should therefore be based upon a very large number of observations,
employing the best instruments that are available, and tne various sights being so
taken that probable errors are offset in reckoning the mean.
4:4:6. By taking a number of sights the observer arrives at the most probable
result of which his instruments and his own faculties render him capable; but this
result is liable to an error whose amount is indeterminate and which is equal to the
algebraic sum of a number of small errors due, respectively, to his instruments
(which must always lack perfection in some details), to an improper allowance for
refraction under existing atmospheric conditions, and to his own personal error.
Aissuming, as we may, that the personal error is approximately constant, these
three causes give rise to an error by which all altitudes appear too great or too small
by a uniform but unknown amount. Let us assume, for an illustration, that this
error has the effect of making all altitudes appear 30* too great; if an observer
attempted to work his latitude from the meridian altitude of a star bearing south,
the result of this unknown error would give a latitude 30* south of the true latitude;
202 MARINE SURVEYING.
if another star to the southward were observed, this mistake would be repeated;
but if a star to the north were taken, the resulting latitude would be 30" to the
north. It is evident, therefore, that the true latitude will be the mean of the results
of observation of the northern and the southern star, or the mean of the average of
several northern stars and the average of several southern stars. A similar process
of reasoning will show that errors in the determination of hour angle are offset by
taking the mean of altitudes of objects respectively east and west of the meridian.
447. It must be remembered that the uniformity of the unknown error only
exists where the altitude remains approximately the same, as instrumental and refrac
tion errors may vary with the altitude ; another condition of uniformity requires that
the instrument and the observer remain the same, and that all observations be taken
about the same time, in order that atmospheric conditions remain unchanged; to
preserve uniformity, if the artificial horizon is used, the same end of the roof should
always be the near one to the observer; in taking the sun, however, as the personal
error may not be the same for approaching as for separating limbs, every series of
observations should be made up of an equal number of sights taken under each
condition.
448. With all of this in mind, we arrive at the general rule that astronomical
determinations shall be based upon the mean of observations, under similar conditions,
of bodies whose respective distances from the zenith are nearly equal, and which
bear in opposite directions therefrom.
449. This condition eliminates the sun from availability for observations for
latitude, though it properly admits the use of that body for longitude where equal
altitudes or single a. m. and p. m. sights are taken. Opposite stars of approximately
equal zenith distance should always be used for latitude, circum-meridian altitudes
being observed during a few minutes before and after transit; excellent results are
also obtained from stellar observations for longitude; but very low stars should be
avoided, on account of the uncertainty of refraction, and likewise very high ones,
as the reflection from the index mirror of the sextant may not be perfectly distinct
when the ray strikes at an acute angle.
If there is telegraphic or radio communication, an endeavor should be made
to obtain a time signal from a reliable source, instead of depending upon the
chronometers.
450. TOPOGRAPHY. The plane table, with telemeter and stadia, affords the
most expeditious means of plotting the topography, and should be employed when
available. Points on shore may also be plotted by sextant angles, using the three-
point problem, or by any other reliable method.
451. HYDROGRAPHY. The correct delineation of the hydrographic features
being one of the most important objects of the survey, great care should be devoted
to this part of the work. Soundings are run in one or more series of parallel lines,
the direction and spacing of which depend upon the scope of the survey. It is
usual for one series of lines to extend in a direction normal to the general trend of the
shore line. In most cases a second series runs perpendicular to the first, and in surveys
of important bodies of water still other series of lines cross the system diagonally.
In developing rocks, shoals, or dangers the direction of the lines is so chosen as will
best illustrate the features of the bottom. When lines cross, the agreement of the
reduced soundings at their intersection affords a test of the accuracy of the work.
As the depth of water increases, if there is no reason to suspect dangers, the
interval between lines may be increased.
Lines are run by the ship or boat in such manner as to follow as closely as possible
the scheme of sounding that has been laid out. The position is located by angles
at the beginning of each line, at each change of course, at frequent intervals along
the ^ line, and at the point where each line is finished. Soundings taken between
positions are plotted by the time intervals or patent log distances.
452. There are a number of methods for determining positions while sounding,
which may be described briefly as follows:
By two sextant angles. Two observers with sextants measure simultaneously
the angles between three objects of known position, and the position is located by
the three-point problem. This is the method most commonly employed in boat
work, and has the great advantage that the results may be plotted at once on the
MARINE SURVEYING.
203
working sheet in the boat and the lines as run thus kept nearly in coincidence with
those laid out in the scheme. A study of the three-point problem (art. 153, Chap.
IV) will give the considerations that must govern in the selection of objects.
By two theodolite angles. Two stations on shore are occupied by observers with
theodolites, and at certain instants, indicated by a signal from the ship or boat, they
observe the angular distance thereof from some known point. The intersection
of the direction lilies thus given is at the required position. This method is expedi
tious where the signals are small or not numerous. Its disadvantage is that the
plotting can not be kept up as the work proceeds.
By one sextant and one theodolite angle. An observer ashore occupies a station
with a theodolite and cuts in the ship or boat, while one on board takes a sextant
angle between two objects, of which one should preferably be the occupied station.
It is plotted by laying off the direction line from the theodolite and finding with a
three-armed protractor or piece of tracing paper at what point of that line the
observed angle between the ob
jects is subtended. Its advantages
and disadvantages are the same as
those of the preceding method.
In running lines of soundings
offshore, where signals are lost
sight of, the best method is to get
an accurate departure, before drop
ping the land, by the best means
that offers, keeping careful note
of the dead reckoning, and on run
ning in again, to get a position as
soon as possible, note the drift and
reconcile the plotting of inter
mediate sounoings accordingly.
Where circumstances require, the
position may be located by astro
nomical observations as usually
taken at sea.
453. A careful record of sound
ings must be kept, showing the
time of each (so that proper tidal
correction may be applied), the
depth, the character of bottom, and
such data as may be required to
locate the position.
454. THE WIRE DRAG. The
use of the lead in hydrographic
surveying does not absolutely es
tablish a definite available depth,
as pinnacle obstructions may exist which are not detected by that means. This is
particularly true of rocky localities and those of coral formation.
In order to guarantee a certain depth of water for purposes of navigation it has
become the practice to tow through the waters to be examined a line of wire or cable
suspended at that depth.
The drag or sweep consists essentially of a horizontal member, known as the
bottom wire, which is a long steel line composed of 50-foot sections coupled together
with swivels and shackles. It is supported at each terminal from an 80-pound buoy
by a chain stirrup fine whose length may be adjusted from 20 to 50 feet. There
are smaller buoys placed at intervals varying from 150 to 450 feet, according to local
conditions, which support the \yire by means of steel-cable stirrup lines, adjustable
in length like the chain stirrup lines on the terminal buoys. At intermediate 50-foot
connections, cedar toggles or floats, which have a little more buoyancy than is
sufficient to support the wire between the stirrup lines, are attached by means of
snap hooks. To prevent the bottom wire from sagging back as the drag is towed
transversely to its own length by the bridles fastened at the terminals, a leaden
FIG. 67.
204
MAKINE SURVEYING.
weight of 165 pounds is suspended from each of the terminal stirrup lines, and a
weight of 20 pounds from each of the intermediate stirrup lines. The length of the
drag may be varied through a wide range to suit the conditions existing in the
localities to be examined. Any multiple of 50 feet may be used, but it is in general
found best to use, in each division between two towing launches, eight sections with
stirrup-line suppports at their ends, each composed of from three to seven 50-foot
units. The towing launches use tow lines about 200 feet in length bridled to the
terminal stirrup lines with attachments at the top and bottom. During the towing, as
long as the drag is free, the line of supporting buoys will trace out a parabolic curve
on the surface of the water; but, if progress should be interrupted by a pinnacle of
rock rising in its path above the depth to which the drag line is set, the parabolic
curve of the line of buoys will immediately become broken into the form of a V,
whose angle will correspond in position with the position of the pinnacle. . The pres
ence of any such obstruction is also registered by the spring balance usually attached
to the towline at a convenient position near the towing vessel. If the shape of the
obstruction is such as to allow tne drag line to ride upward upon it, as may be with
bowlders and shoals, an additional indication of its presence is afforded by the f ailing
over of the supporting buoys when the suspended stirrup lines are
relieved of strain by the grounding of the weights attached to them.
In such cases a tender should be in readiness to proceed to the
indicated point for the purpose of taking position angles to locate
the spot and also soundings to ascertain the characteristics of the
obstruction. Such localities are plotted upon the chart upon
which the paths of the drag line are being mapped, and later these
areas are again swept with the drag line at a lesser depth;" and
this procedure is continued until the obstruction is cleared by the
dragline, and thus the least depth is proved. The position of the
drag is determined by observers with sextants on board the towing
vessels who simultaneously measure, at frequent intervals, the
values of two angles between two pairs of known objects whose posi
tions are identified upon the plotting chart.
The average speed of towing is about 1J knots per hour, and
the average area explored per working day is 1J square miles,
although a much higher rate of progress is usually attained hi open
areas under favorable conditions.
455. TIDAL OBSERVATIONS. These should begin as early as
practicable and continue throughout the survey, it being most im
portant that they shall, if possible, cover the period of a lunar month. In the chap
ter on tides (Chap. XX) the nature of the data to be obtained is explained.
456. MAGNETIC OBSERVATIONS. The feature of the earth s magnetism with
which the navigator is most concerned is the variation, which is set forth on the
chart, and upon the determination of which will depend the correctness of all courses
and bearings on shipboard. It is usually obtained by noting the compass direction
from the observation spot of the object whose true bearing is known by calculation,
and comparing the true and compass bearings; or it may be observed by mounting
the ship s compass in a place on shore free from foreign magnetic influence, and finding
the compass error as it is found on board. Observations for dip and intensity are
also made when the proper instruments are at hand.
457. KUNNING SURVEY. Where time and opportunity permit only a superficial
examination of a coast line or water area, or where the interests of navigation require
no more, recourse is had to a running survey, in which shore positions are determined
and soundings are made while the ship steams along the coast, stopping only occa
sionally to fix her position, and in which the assistance of boat or shore parties may
or may not be employed.
In this method the ship starts at one end of the field from a known position,
fixed either by astronomical observations or by angles or bearings of terrestrial
objects having a determined location. Careful compass bearings or sextant angles
are taken from this position to all objects ashore which can be recognized, and a
series of direction lines is thus obtained. The ship then steams along tne coast, at a
convenient distance therefrom, keeping accurate account of her run by compass
FIG. 68.
MAKINE SURVEYING. 205
courses and patent log. From time to time other series of bearings or angles are
taken upon those objects ashore which are to be located, the direction lines plotted
from the estimated position of the ship, and the various objects located by the
intersections with their other direction lines. During all the time that the ship is
under way, soundings are taken at regular intervals and plotted from the dead reck
oning. As frequently as circumstances permit, the ship is stopped and her position
located by the best available means, and the intervening dead reckoning reconciled
for any current that may be found.
If a steam launch can be employed in connection with a running survey, it is
usually sent to run a second line inshore of the ship. The boat s position is obtained
by bearings of objects ashore which are located by the ship, or by bearings and mast
head angles of the ship, or by such other means as offer. The duty of the boat is
to take a series of soundings and to collect data for shore line and topography.
If circumstances allow the landing of a shore party, its most important duty is
to mark the various objects on shore by some sort of signals w r hich will render them
unmistakable. Beyond this, it can perform such of the duties assigned to shore
parties in a regular survey as opportunity permits.
CHAPTER XVIII.
WINDS,
458. Wind is air in approximately horizontal motion. Observations of the
wind should include its true direction, and its force or velocity. The direction of the
wind is designated by the point of the compass from which it proceeds. The force
of the wind is at sea ordinarily expressed in terms of the Beaufort scale, each degree
of this scale corresponding to a certain velocity in miles per hour, as explained in
article 68, Chapter II.
459. THE CAUSE OF THE WIND. Winds are produced by differences of atmos
pheric pressure, which are themselves ultimately, and in the main, attributable to
differences of temperature.
To understand how the air can be set in motion by these differences of pressure,
it is necessary to have a clear conception of the nature of the air itself.
The atmosphere which completely envelops the earth may be considered as a
fluid sea at the bottom of which we live, and which extends upward to a considerable
height, probably 200 miles, constantly diminishing in density as the altitude increases.
The air, or material of which this atmosphere is composed, is a transparent gas,
which, like all other gases, is perfectly elastic and highly compressible. Although
extremely light, it has a perfectly definite weight, a cubic foot of air at ordinary
pressure and temperature weighing 1.22 ounces, or about one seven hundred and
seventieth part of the weight of an equal volume of water. In consequence of this
weight it exerts a certain pressure upon the surface of the earth, amounting on the
average to 15 pounds for each square inch. To accurately measure this pressure,
which is constantly undergoing slight changes, we ordinarily employ a mercurial
barometer (art. 48, Chap. II), an instrument in which the weight of a column of air
of given cross section is balanced against that of a column of mercury having an
equal cross section; and instead of saying that the pressure of the atmosphere is a
certain number of pounds on each square inch, we say that it is a certain number of
inches of mercury, meaning thereby that it is equivalent to the pressure of a column
of mercury that many inches in height, and one square inch in cross section.
All gases, air included, are highly sensitive to the action of heat, expanding or
increasing in volume as the temperature rises, contracting or diminishing in volume
as the temperature falls. Suppose now that the atmosphere over any considerable
region of the earth s surface is maintained at a higher temperature than that of its
surroundings. The warmed air wih 1 expand, and its upper layers will flow off to the
surrounding regions, cooling as they go. The atmospheric pressure at sea level
throughout the heated areas will thus be diminished, while that over the circum
jacent cooler areas will be correspondingly increased. As the result of this difference
of pressure, there will be movement of the surface air away from the region of high
pressure and toward the region of low, somewhat similar to the flow of water which
takes place through the connecting bottom sluice as soon as we attempt to fill one
compartment of a divided vessel to a slightly higher level than that found in the
other.
A difference of atmospheric pressure at sea level is thus immediately followed
by a movement of the surface air, or by winds ; and these differences of pressure have
their origin in differences of temperature. If the atmosphere were everywhere of
uniform temperature it would lie at rest on the earth s surfaces-sluggish, torpid,
and oppressive and there would be no winds. This, however, is fortunately not
the case. The temperature of the atmosphere is continually or periodically higher
in one region than in another, and the chief variations in the distribution of tempera
ture are systematically repeated year after year, giving rise to like systematic
variations in the distribution of pressure.
206
WINDS. 207
460. THE NORMAL DISTRIBUTION OF PRESSURE. The winds, while thus due
primarily to differences of temperature, stand in more direct relation to differences
of pressure, and it is from this point of view that they are ordinarily studied.
In order to furnish a comprehensive view of this distribution of atmospheric
pressure over the earth s surface, charts have been prepared showing the average
reading of the barometer for any given period, whether a month, a season, or a year,
and covering as far as possible the entire globe. These are known as ispbaric charts,
from the fact that all points at which the barometer has the same reading are joined
by a continuous line or isobar.
The isobaric chart for the year (fig. 69) shows in each hemisphere a well-defined
belt of high pressure (30.20 inches) completely encircling the globe, that in the northern
hemisphere naving its middle line about in latitude 35 North, that in the southern
hemisphere about in latitude 30 South, these constituting the so-called meteorological
tropics. From the summit or ridge of each of these belts the pressure falls off alike
toward the equator and toward the pole, although much less rapidly in the former
direction than in the latter. The equator itself is encircled by a belt of somewhat
diminished pressure (29.90 inches), the middle line of which is ordinarily found in
northern latitudes. In the northern hemisphere the diminution of pressure on the
poleward slope is much less marked and much less regular than in the southern
hemisphere, minima (29.70 inches) occurring in the North Atlantic Ocean near
Iceland and in the North Pacific Ocean near the Aleutian Islands, beyond which the
pressure increases. In the southern hemisphere no such minima are apparent, the
pressure continuing to diminish uninterruptedly as higher and higher latitudes are
attained. Along the sixtieth parallel of south latitude the average barometric
reading is 29.30 inches.
461. SEASONAL VARIATIONS OF PRESSURE. As might be expected from its
close relation to the temperature, the whole system of pressure distribution exnibits
a tendency to foUow the sun s motion in declination, the barometric equator occupy
ing in July a position slightly to the northward of its position in January. In either
hemisphere, moreover, the pressure over the land during the winter season is decidedly
above the annual average, during the summer season decidedly below it ; the extreme
variations occurring in the case of continental Asia, where the mean monthly pressure
ranges from 30.50 inches during January to 29.50 inches during Jul} r . ^Over the
northern ocean, on the other hand, conditions are reversed, the summer pressures
being here somewhat the higher. Thus, in January the Icelandic and the Aleutian
minima increase in depth to 29.50 inches, while in July these minima fill up and are
well-nigh obliterated, a fact which has much to do with the strength and frequency
of the winter gales in high northern latitudes and the absence of these gales during
the summer. Over the southern ocean, in keeping with its slight contrast between
winter and summer temperatures, similar variations of pressure do not exist.
462. THE PREVAILING WINDS. As a result of the distribution of pressure just
described, there is in either hemisphere a continual motion of the surface air away
from the meteorological tropic on one side toward the equator, on the other side
toward the pole, the first constituting in each case the trade winds, the second the
prevailing winds of higher latitudes. Upon a stationary earth the direction of this
motion would be immediately from the region of high toward the region of low
barometer, the moving air steadily following the barometric slope or gradient,
increasing in force to a gale where these gradients are steep, decreasing to a light
breeze where they are gentle, sinking to a calm where they are absent. The earth,
however, is in rapid rotation, and this rotation gives rise to a force which exercises
a material influence over all horizontal motions upon its surface, whatever their
direction, serving constantly to divert them to the right in the northern hemisphere,
to the left in the southern. The air set in motion by the difference of pressure is
thus constantly turned aside from its natural course down the barometric gradient
or slope, and the direction of the wind at any point, instead of being identical with
that of the gradient at that point, is deflected by a certain amount, crossing the
latter at an angle which in practice varies between 45 and 90 (4 to 8 compass
points), the wind in the latter case blowing parallel to the isobars. As a consequence
of this deflection the northerly winds winch one would naturally expect to find on
the equatorial slope of the belt of high pressure in the northern hemisphere become
208
WINDS.
FIG. 69.
WINDS. 209
northeasterly the NE. trade; the southerly winds of the polar slope become south
westerly the prevailing westerly winds of northern latitudes. So, too, for the
southern hemisphere, the southerly winds of the equatorial slope here becoming
southeasterly the SE. trades; the northerly winds of the polar slope northwesterly
the prevailing westerly winds of southern latitudes.
463. The relation here described as existing between the distribution of atmos
pheric pressure and the direction of the wind is of the greatest importance. It may
be briefly stated as follows:
In the northern hemisphere stand with the face to the wind; in this position
the region of high barometer lies on your left hand and somewhat in front of you;
the region of low barometer on your right hand and somewhat behind you.
In the southern hemisphere stand with the face to the wind; in this position
the region of high barometer lies on your right hand and somewhat in front of you ;
the region of low barometer on your left hand and somewhat behind you.
This relation holds absolutely, not only in the case of the general distribution of
pressure and circulation of the atmosphere, but also in the case of the special con
ditions of high and low pressure which usually accompany severe gales.
464. THE TRADE WINDS. The Trade Wwds blow from the tropical belts of
high pressure toward the equatorial belt of low pressure in the northern hemisphere
from the northeast, in the southern hemisphere from the southeast. Over the
eastern half of each of the great oceans they extend considerably farther from the
line and their original direction inclines more toward the pole than in midocean,
where the latter is almost easterly. They are ordinarily looked upon as the most
constant of winds, but while they may blow for days or even for weeks with slight
variation in direction or strength, their uniformity should not be exaggerated.
There are times when the trade winds weaken or shift. There are regions where
their steady course is deformed, notably among the island groups of the South Pacific,
where the trades during January and February are practically nonexistent.
They attain their highest development in the South Atlantic and in the South Indian
Ocean, and are everywhere fresher during the winter than during the summer season.
They are rarely disturbed by cyclonic storms, the occurrence of the latter within the
limits of the trade-wind region being furthermore confined in point of time to the
late summer and autumn months of the respective hemispheres, and in scene of
action to the western portion of the several oceans. The South Atlantic Ocean
alone, however, enjo}*s complete immunity from tropical cyclonic storms.
465. THE DOLDRUMS. The equatorial girdle of low pressure occupies a position
between the high-pressure belt of the northern and the similar belt 01 the southern
hemisphere. Throughout the extent of this barometric trough the pressure, save
for the slight diurnal oscillation, is practically uniform, and decided barometric
gradients do not exist. Here, accordingly, the winds sink to stagnation, or rise at
most only to the strength of fitful breezes, coming first from one point of the compass,
then from another, with cloudy, rainy sky and frequent thunderstorms. The region
throughout which these conditions prevail consists of a wedge-shaped area, the base
of the wedge resting in the case of the Atlantic Ocean on the coast of Africa, and in
the case of the Pacific Ocean on the coast of America, the axis extending westward.
The position and extent of the belt vary somewhat with the season. Throughout
February and March it is found immediately north of the equator and is of inap
preciable width, vessels following the usual sailing routes frequently passing from
trade to trade without interruption in both the Atlantic and the Pacific Oceans.
In July and August it has migrated to the northward, the axis extending east and
west along the parallel of 7 north, and the belt itself covering several degrees of
latitude, even at its narrowest point. At this season of the year, also, the southeast
trades blow with diminished freshness across the equator and well into the northern
hemisphere, being here diverted, however, by the effect of the earth s rotation, into
southerly and southwesterly winds, the so-called southwest monsoon of the African
and Central American coasts.
466. THE HORSE LATITUDES. On the outer margin of the trades, corresponding
vaguely with the summit of the tropical ridge of high pressure hi either hemisphere,
is a second region throughout which the barometric gradients are faint and undecided,
61828 1C 14
210 WINDS.
and the prevailing winds correspondingly light and yariable ; the so-called horse
latitudes, or calms of Cancer and of Capricorn. Unlike the doldrums, however,
the weather is here clear and fresh, and the periods of stagnation are intermittent
rather than continuous, showing none of the persistency which is so characteristic
of the equatorial region. The explanation of this difference will become obvious
as soon as we come to study the nature of the daily barometric changes of pressure
in the respective regions, these in the one case being marked by the uniformity of the
torrid zone, in the other sharing to a limited extent in the wide and rapid variations
of the temperate.
467. THE PREVAILING WESTERLY WINDS. On the exterior or polar side of the
tropical maxima the pressure again diminishes, the barometric gradients beinsj now
directed toward the pole; and the currents of air set in motion along these gradients,
diverted to the right and left of their natural course by the earth s rotation, appear in
the northern hemisphere as southwesterly winds, in the southern hemisphere as
northwesterly the prevailing westerly winds of the temperate zone.
Only in the southern hemisphere do these winds exnibit anything approaching
the persistency of the trades, their course in the northern hemisphere being subject
to frequent local interruption by periods of winds from the eastern semicircle. Thus
the tabulated results show that throughout the portion of the North Atlantic included
between the parallels 40-50 North, and the meridians 10-50 West, the winds
from the western semicircle (South NNW.) comprise about 74 per cent of the
whole number of observations, the relative frequency being somewhat higher in
winter, somewhat lower in summer. The average force, on the other hand, decreases
from force 6 to force 4* Beaufort scale, with the change of season. Over the sea in the
southern hemisphere such variations are not apparent; here the westerlies blow
through the entire year with a steadiness little less than that of the trades them
selves, and with a force which, though fitful, is very much greater, their boisterous
nature giving the name of the " Roaring Forties" to the latitudes in which they are
most frequently observed.
The explanation of this striking difference in the extra- tropical winds of the two
halves of the globe is found in the distribution of atmospheric pressure, and in the
variations which this latter undergoes in different parts of the world. In the landless
southern hemisphere the atmospheric pressure after crossing the parallel of 30
South diminishes almost uniformlv toward the pole, and is rarely disturbed by those
large and irregular fluctuations which form so important a factor in the daily weather
of the northern hemisphere. Here, accordingly, a system of polar gradients exists
quite comparable in stability with the equatorial gradients which give rise to the
trades; and the poleward movement of the air in obedience to these gradients,
constantly diverted to the left by the effect of the earth s rotation, constitutes the
steady westerly winds of the south temperate zone.
468. THE MONSOON WINDS. The air over the land is warmer in summer and
colder in winter than that over the adjacent oceans. During the former season the
continents thus become the seat of areas of relatively low pressure ; during the latter
of relatively high. Pressure gradients, directed outward during the winter, inward
during the summer, are thus established between the land and the sea, which exercise
the greatest influence over the winds prevailing in the region adjacent to the coast.
Thus, off^the Atlantic seaboard of the United States southwesterly winds are most
frequent in summer, northwesterly^ winds in winter; while on the Pacific coast the
reverse is true, the wind here changing from northwest to southwest with the advance
of the colder season.
The most striking illustration of winds of this class is presented by the monsoons
(Mausum, season) of the China Sea and of the Indian Ocean. In January abnormally
low temperatures and high pressure obtain over the Asiatic plateau, high tempera
tures and low pressure over Australia and the nearby portion of the Indian Ocean.
As a result of the baric gradients thus established, the southern and eastern coast
of the vast Asiatic continent and the seas adjacent thereto are swept by an outflowing
current of air, which, diverted to the right of the gradient by the earth s rotation,
appears as a northeast wind, covering the China Sea and the northern Indian Ocean.
Upon entering the southern hemisphere, however, the same force which hitherto
WINDS. 211
deflected the moving air to the right of the gradient now serves to deflect it to the
left; and here, accordingly, we have the monsoon appearing as a northwest wind,
covering the Indian Ocean as far south as 10, the Arafura Sea, and the northern
coast of Australia,
In July these conditions are precisely reversed. Asia is now the seat of high
temperature and correspondingly low pressure," Australia of low temperature aiid
high pressure, although the departure from the annual average is by no means so
pronounced in the case of the latter as in that of the former. The baric gradients
thus lead across the equator and are addressed toward the interior of the greater
continent, giving rise to a system of winds whose direction is southeast in the southern
hemisphere, southwest in the northern.
The northeast (winter) monsoon blows in the China Sea from October to April,
the southwest (summer) monsoon from May to September. The former is marked
by all the steadiness of the trades, often attaining the force of a moderate gale; the
latter appears as a light breeze, unsteady in direction, and often sinking to a calm.
Its prevalence is frequently interrupted by tropical eye Ionic storms, locally known
as typhoons, although the occurrence of these latter may extend well into the season
of the winter monsoon.
469. LAND AND SEA BREEZES. Corresponding with the seasonal contrast of
temperature and pressure over land and water, there is likewise a diurnal contrast
which exercises a similar though more local effect. In summer particularly, the land
over its whole area is warmer than the sea by day, colder than the sea by night, the
variations of pressure thus established, although insignificant, sufficing to evoke a
system of littoral breezes directed landward during the daytime, seaward during the
night, which, in general, do not penetrate to a distance greater than 30 miles on and
oft shore, and extend but a few hundred feet into the depths of the atmosphere.
The sea breeze begins in the morning hours from 9 to 11 o clock as the land
warms. In the late afternoon it dies away. In the evening the land breeze springs
up, and blows gently out to sea until morning. In the tropics this process is repeated
day after day with great regularity. In our own latitudes, the land and sea breezes
are often masked by winds of cyclonic origin.
470. A single important effect of the seasonal variation of temperature and
pressure over the land remains to be described. If there were no land areas to break
the even water surf ace. of the globe, the trades and westerlies of the terrestrial circu
lation would be developed in the fullest simplicity, with linear divisions along latitude
circles between the several members a condition nearly approached in the land-
barren southern hemisphere during the entire year, and in tne northern hemisphere
during the winter season. In the summer season, however, the tropical belt of high
pressure is broken where it crosses the warm land, and the air shouldered off from
the continents accumulates over the adjacent oceans, particularly in the northern
or land hemisphere. This tends to create over each of the oceans a circular or
elliptical area of high pressure, from the center of which the baric gradients radiate
in all directions, giving rise to an outflowing system of winds, whicn by the effect of
the earth s rotation is converted into an outflowing spiral eddy or anticyclonic whirl.
The sharp lines of demarcation which would otherwise exist between the several
members of the general circulation are thus obliterated, the southwesterly winds of the
middle northern latitudes becoming successively northwesterly, northerly, and north
easterly, as we approach the equator and round the area of high pressure by the east;
the northeast trade becoming successively southeasterly, southerly, and southwesterly,
as we recede from the equator and round this area by the west ; similarly for the other
hemisphere.
CHAPTER XIX.
CYCLONIC STOEMS,
471. VARIATIONS OF THE ATMOSPHERIC PRESSURE. The distribution of the
atmospheric pressure previously described ((hap. XVIII) and the attendant circu
lation of the winds are those which become evident after the effects of many disturbing
causes have been eliminated by the process of averaging, or embracing in the sum
mation, observations covering an extended period of time. The distribution of
pressure and the system of winds which actually exist at a given instant will in
general agree with these in its main features, but may differ from them materially
in detail.
Confining our attention for the time being to the subject of atmospheric pressure,
it may be said that this, at any given point on the earth s surface, is in a constant
state of change, the mercurial barometer rarely becoming stationary, and then only
for a few hours in succession. The variations which the pressure undergoes may
be divided into two classes, viz, periodic, or those which are continuously in opera
tion, repeating themselves within fixed intervals of time, long or short; and non-
periodic or accidental, which occur irregularly, and are of varying duration and
extent.
472. PERIODIC VARIATIONS. Of the former class of changes the most important
are the seasonal, which have been already to some extent described, and the diurnal.
The latter consists of the daily occurrence of two barometric maxima, or points of
highest pressure, with two intervening minima. Under ordinary circumstances
with the atmosphere free from disturbances, the barometer each day attains its first
minimum about 4 a. m. As the day advances the pressure increases, and a maximum,
or point of greatest pressure, is reached about 10 a. m. From this time the pressure
diminishes, and a second minimum is reached about 4 p. m., after which the mercury
again rises, reaching its second maximum about 10 p. m. " The range of this diurnal
oscillation is greatest at the equator, where it amounts to ten hundredlhs (0.10) of
an inch. It diminishes with increased latitude, and near the poles it seems to vanish
entirely. In middle latitudes it is much more apparent in summer than in winter.
473. NONPERIODIC VARIATIONS. The equatorial slope of the tropical belt of
high pressure which encircles the globe in either hemisphere is characterized by the
marked uniformity of its meteorological conditions, the temperature, wind, and
weather changes proper to any given season repeating themselves as day succeeds
day with almost monotonous regularity. Here the diurnal oscillation of the barom
eter constitutes the main variation to which the atmospheric pressure is subjected.
On the polar slope of these belts conditions the reverse of these obtain, the elements
which go to make up the daily weather here passing from phase to phase without
regularity, with the result that no two days are precisely alike; and as regards
atmospheric pressure, it may be said that in marked contrast with the uniformity of
the torrid zone, the barometer in the temperate zone is constantly subjected to non-
periodic or accidental fluctuations of such extent that the periodic diurnal variation
is scarcely apparent, the mercurial barometer at a given station frequently rising or
falling several tenths of an inch in twenty-four hours.
474. PROGRESSIVE AREAS OF HIGH AND Low PRESSURE. The explanation of
this rapid change of conditions is found in the approach and passage of extensive
areas of alternately high and low pressure, which affect alike, although to a different
degree, all the barometers coming within their scope. The general direction of
motion of these areas is that of the prevailing winds; eastward, therefore, in the
latitudes which are under consideration.
Taken in conjunction, these areas of high and low pressure exercise a controlling
influence over the weather changes of the temperate zones. As the low area draws
212
CYCLONIC STORMS.
213
near, the skv becomes overclouded, the prevailing westerly wind falls away, and
is succeeded by a wind from some easterly direction, faint at first, but increasing as
the pressure continues to diminish; the lowest pressure having been reached, the
wind again goes to the westward, the barometer starts to rise, and the weather clears;
all marking the eastward recession of the low area and the approach of the subsequent
high.
The first stage in the development of the low is a slight diminution of the
atmospheric pressure, amounting in general to not more than one or two hundredths
of an inch, throughout an area covering a more or less extensive portion of the earth s
surface, either land or water, but far more frequently over the former than over the
latter. Shortly after the advent of this, initiatory fall the decrease of pressure
throughout some small region within the larger area assumes a more decided character,
the mercury here standing at a lower level than elsewhere and reading successively
higher as we go outward, the region thus becoming, as it were, the center of the whole
barometric depression. A system of barometric gradients is by this means estab
lished, all directed radially inward, and in obedience to these gradients there is a
movement of the surface air toward the center or point of lowest barometer. The
air once in motion, however, the effect of the earth s rotation is brought into play
precisely as in the case of the larger movements of the atmosphere, with the result
that the several currents, instead of following the natural course alon<* these gradients,
are deflected from them, in the northern hemisphere to the right hand., in the southern
hemisphere to the left, the extent of the deflection being from 4 to 8 compass points.
Anticyclonic.
NORTHERN HEMISPHERE.
Cyclonic.
Anticyclonic.
Cyclonic.
SOUTHERN HEMISPHERE.
FIG. 7\
The light arrows show the direction of the gradients; the heavy arrows the direction of the winds.
475. CYCLONES AND CYCLONIC CIRCULATIONS. A central area of low barometer
will thus be surrounded by a system of winds which constantly draw in toward the
center but at the same time circulate about it, the whole forming an inflowing spiral;
the direction of this circulation being in the southern hemisphere with the motion
of the hands of a watch, in the northern hemisphere opposed to this motion. Where
the barometric gradients are steep, these winds are apt to be strong; where they are
gentle, the winds are apt to be weak; where they are absent, as is the case at the
center or bottom of the depression, calms are apt to prevail.
Around the center of the area of high pressure a similar system of wind will be
found, but blowing in a contrary direction. Here the barometric gradients are
directed radially outward, with the result that in place of the inflowing, we have an
outflowing spiral, the circulatory motion being right handed or with the hands of
a watch in the northern hemisphere, left handed or against the hands of a watch in
the southern.
All these features are shown in the accompanying diagrams (fig. 70), which
exhibit the general character of cyclonic (around the low) and anticyclonic (around
the high) circulations in the northern and the southern hemisphere, respectively.
214
CYCLONIC STORMS.
The closed curves represent the isobars, or linos along which the barometric pressure
is the same; the short arrows show the direction of the gradients, which are every
where at right angles to the isobars; the long arrows give the direction of the winds,
deflected by the earth s rotation to the right of the gradients in the northern hemi
sphere, to the left in the southern.
476. FEATURES OF CYCLONIC AND ANTICYCLONIC REGIONS. Certain features of
the two areas may here be contrasted. In the anticyclonic, the successive isobars
are as a rule far apart, showing weak gradients and consequently light winds; the
areas themselves are of relatively great extent, and their rate of progression is slow.
During the summer they originate as extensions into higher latitudes of the margins
of the tropical belts of high pressure; during the winter, as offshoots of the strong
anticyclone which covers the land throughout that season. Their approach and
presence is accompanied by polar or westerly winds, temperature below the seasonal
average, fair weather, and clear skies. In the cyclonic area the successive isobars
are crowded together, showing steep gradients and strong winds; they may appear
either as trougn-like extensions into the temperate zone of the polar belt of low
pressure, in which case the easterly winds proper to their polar side are nonexistent,
or (in lower latitudes) as independent areas, sometimes, indeed, as detached portions
of the equatorial low-pressure belt, which move eastward and poleward across the
temperate zone, and are ultimately merged into the great cyclonic area surrounding
the pole. The progress of these independent areas is invariably attended by the
strong and steadily shifting winds, foul weather, and other features which make up
the ordinary storm, at sea. In the trough-like depressions of higher latitudes these
features may or may not be observed, their presence depending upon the depths of
the barometric trough and the steepness of its slopes. In these, moreover, the
cyclonic circulation is never completely developed, the storm winds having rather
the character of right line gales, blowing from an equatorial or easterly direction
until the axis of the trough is at hand, and as this passes shifting by the west at one
bound to a polar direction.
477. CYCLONIC STORMS. Strong winds are the result of steep barometric
gradients. These may occur with cyclonic or with anticyclonic areas, the latter
being exemplified in the case of the northers in the Gulf of Mexico and the north
westerly winter gales along the Atlantic coast of the United States, which are almost
invariably accompanied by barometers above the average. They are, however, so
much more frequent in the case of areas of low pressure and consequent cyclonic
circulations, with their attendant foul-weather characteristics, that the latter are
generally known as cyclonic storms, i. e., storms in which the wind circulation is
cyclonic.
Cyclonic storms may with convenience be divided into two classes: viz, tropical,
or those which originate near but not on the equator; and extra-tropical, or those
which first appear in higher latitudes.
478. TROPICAL CYCLONIC STORMS. The occurrence of tropical cyclonic storms
is confined to the summer and autumn months of the respective hemispheres, and to
the western part of the several oceans, the North Atlantic, the North Pacific, the
South Pacific, and the Indian Ocean. They are unknown in the South Atlantic
Ocean. -Although these cyclonic storms are all of the same essential characteristics,
they have generally been called hurricanes when occurring in the West Indies and the
region between Samoa and Australia, typhoons when occurring in the region of the
Philippines, and cyclones when occurring in the Indian Ocean and its dependent seas.
The limits of the regions within which these tropical storms originate are defined
by parallels of latitude and meridians of longitude as follows :
Latitude.
Longitude from
Greenwich.
Hurricanes of the West Indies
12 to 28 N
55 to 95 W.
Typhoons of the Philippine region
5 to 20 N
150 to 115 E.
Cyclones of the Bay of Bengal
8 to 22 N
100 to 80 E
Cyclones of the Indian Ocean
4 to 30 S
100 to 40 E
Hurricanes of the Samoan region
10 to 30 S
160 W. to 150 E.
CYCLONIC STORMS.
215
The percentage of frequency of these storms in the different months of the year
is set forth in the following: table:
Jan.
Feb.
Mar.
Apr.
2
15
6
May.
June.
Julv.
Aug.
25
16
15
Sept.
Oct.
1 rH rH O l^ CO
*S i 1 i 1
5
4
10
13
Hurricanes of the West Indies
2
22
29
0.4
19
17.5
I
18
28
1
5
6
6
1
G
9
12
1
4
16
19.
0.5
32
19
20
1.5
31
14
14
1.5
1
Typhoons of the Philippine region. . . .
t yclones of the Bav of Bengal
(Vclones of the Indian Ocean ....
Hurricanes of the Samoan region
The yearly average number of those occurring in the West Indian region is 4, in
the Philippine region 21, in the Bay of Bengal 9, in the Indian Ocean (south of the
Equator) 9, and in the region between Samoa and Australia 4.
4:79. MOTIOX OF THE STORM CEXTER. In the case of tropical cyclonic storms
there is always a tendency for the barometric depression, impelled by the general
motion of the atmosphere in the trade-wind region, to follow a path which tends at
once westward and away from the equator. This motion continues until the limits
of the trades are reached, where the path ordinarily recurves; and the subsequent
motion of the depression is eastward and toward the pole, the disturbance at the
same time assuming the features of the extra- tropical cyclonic storm.
Rate of progress of the storm center. Within the tropics in the northern hemi
sphere, the average velocity of the storm center along the path is 11 miles an hour;
and in the latitude of the recurvature of the storm this average is maintained,
although there are numerous instances of wide variations in the rate of progress here,
and sometimes the center becomes stationary for a few days. In higher latitudes, the
rate increases to an average of 16 miles an Sour.
In the southern hemisphere, the average velocity of progress as far as determined
is somewhat less than in the northern; and, in the Indian Ocean, many of the Mauri
tius cyclones have a very small movement of translation, and these are, in conse
quence, designated as stationary cyclones.
The general path of the tropical cyclonic storm in either hemisphere and the
cyclonic circulation of the wind about the storm center are given in figures 73 and
74; that for the northern hemisphere applying to the hurricanes of the West Indies;
that for the southern hemisphere to the hurricanes of the South Pacific Ocean.
480. INDICATIONS OF THE APPROACH OF TROPICAL CYCLOXIC STORMS. The
premonitory signs of a tropical cyclonic storm comprise, besides those feelings of
personal discomfort which are common within the sphere of atmospheric disturbance
of cyclonic storms in all parts of the world, (1) an unsteady barometer, or even a
cessation of the diurnal range, which is constant in settled weather; (2) a heavy
swell not caused by the wind then blowing; (3) the appearance of the sky arising
from the forms and movements of the clouds. It is upon the concomitance of these
indications, rather than the recognition of any one of them, that reliance should be
placed.
The appearance of the clouds and their value as storm warnings is described as
follows by Faura in the Cyclones of the Far East, by Jose Algue, of the Manila
Observatory :
The best means for determining the center [of a storm] and for following up its movements are the
observations of cirri, little clouds of a very fine structure and clear opal color, "which appear as elongated
feathers. * * * Long before the least sign of bad weather is noticeable and in many cases when the
barometer is still very high being under the influence of a center of high pressure, which generally
precedes a tempest these small isolated clouds appear in the upper regions of the atmosphere. They
seem to be piled up on the blue vault of heaven and drawn out in the direction of some point on the
horizon toward which they converge. The first to present themselves are few in number but well defined
and of the most delicate structure, appearing like filaments bound together but whose visibility is lost
before they reach the point of radiation. We often had an opportunity to watch them at the observatory
of Manila, when the center was still 600 miles distant. The best times for observing the cirri are sunrise
and sunset. If the sun is in the east and very near the horizon, the first clouds which are tinged by
the solar rays are the cirro-strati which precede the cyclone, and they are also the last to disappear at
sunset, inasmuch as they overspread the horizon. Such times are the best for determining the radiant
point of the cloud streaks and at the same time for ascertaining the direction in which the center lies. Later
on the delicacy of form, which characterizes this class of clouds in its earlier stages, is lost, and the clouds
216
CYCLONIC STORMS.
appear in more confused and tangled forms, like streamers of feather work, with central nuclei, which
etill maintain this direction, so that the point of radiation can still be detected. In order to ascertain
approximately the direction in which the center is advancing in its movement of translation, it is necessary
FIG. 71. Average Paths of Hurricanes in the West Indies.
The small circles indicate the points of origin of 130 storms, which comprise all the instances
resulting from the authentic accounts of a period of 35 years.
June and July storms September storms
August storms Q October storms
to determine the changes of the radiant point at equal intervals of time and to compare them with the
movements of the barometer. If the point of convergence does not perceptibly change its position, but
remains fixed and immovable for a long time, even for several consecutive days, it is almost certain that
CYCLONIC STORMS.
217
the tempest will break over the position of the observer. In this case the barometer begins to fall shortly
after the first cirrus clouds have been observed and sometimes even before. At first it falls slowly, without
JV-
r-> >
120
130
140*
FIG. 72. Mean Paths of Typhoons.
1. Typhoons in the Marianas.
2. Typhoons formed in the Pacific which, at some distance east of the meridian of Manila, have recurved toward
Japan.
3 and 3a. Typhoons formed in the Pacific which, near the meridian of Manila, have recurved toward Japan.
4. Typhoons of Taiwan or Formosa.
5 and oa. Typhoons of northern Luzon which have recurved in the island or near it in the China Sea.
6. Typhoons which have crossed Luzon northward of Manila and continued to the continent.
7. Typhoons which have crossed Luzon southward of Manila.
8. Typhoons of the Visayas and Mindanao.
9. Typhoons formed in the Pacific which have crossed south of Manila, recurved in the China Sea between latitudes
"10 degrees and 20 degrees, and recrossed north of Manila.
10. Typhoons formed in the China Sea.
11. Typhoons formed in the Sulu Sea and the interisland waters.
completely losing the diurnal and nocturnal oscillatory movements, but changing somewhat the hours
of maximum and minimum. The daily reading is observed to be each day less than that of the preceding
218
CYCLONIC STORMS.
Washington
IN HIGH LATITUDES
Velocity- alon; patlx
16 to 30 miles perKcmr
Norfolk
Savsuvnah.
So
30
30
IN MIDDLE LATITUDES
STORM RECURVING
Velocity along patK
11 miles perliour
day. That part of the horizon in the direction of the storm begins to be covered by a cirrus veil, which
increases slowly until it forms an almost homogeneous covering of the sky. This veil is known by the
name "cirro-pallium" of Poe y, and da that which^ causes the solar and lunar halos, which are never
absent when a storm approaches. Beneath the veil a few isolated clouds, commonly called "cotton,"
appear. They are much more numerous and larger on the side lying toward the storm, where they soon
appear as a compact mass. At such times the sunrises and sunsets are characterized by the high red
tint which the clouds assume, resembling a great fire, especially in the direction of the cyclone. The
wind remains fixed at one point, showing only a few variations, which are due principally to the squalls,
which continually exert their force within the limits of the storm. The low or cotton " clouds successively
and from time to time cover the sky, throwing out occasional squalls of rain and wind; but, the squalls
having passed, a lull ensues, the cirrus veil remaining, and like-wise the hurricane bank of clouds, which
seems fixed to the same spot in the direction of the storm. This state of the atmosphere continues until
the bank of clouds invades
QQO 7C) o the point of observation, in
which case the squalls will
be continuous and the wind
will increase in violence each
moment.
The condition of
diminished pressure at
tending a cyclonic
storm gives rise to high
waves which are propa
gated in all directions
from such a storm on
the ocean. These
waves outrun the storm
as^much as a thousand
miles, and, by the di
rection from which they
arrive, indicate the
bearing of the storm s
center.
Although thunder
storms can not be con
sidered as premonitory
signs, it rarely happens
that showers and
squalls are not experi
enced from 24 to 48
hours in advance of the
storm; and the un
settled state of the ba
rometer in the distant
approaches, varying
from 500 to 1,000 miles
in advance of the cen
ter, gives place, at a
distance of 300 to 400
miles, to a slow and steady fall of the mercurial column. At the same time the
direction and velocity of the lower clouds show unmistakable evidence of the
presence of a storm and the bearing of the center. When the storm center is
still far distant, the phenomenon called the "bar of the cyclone ;; may frequently be
seen. This is a dense mass of rain cloud formed about the center of the storm,
giving the appearance of a huge bank of black clouds resting upon the horizon, which
may^ retain its form unchanged for hours. It is usually most conspicuous about
sunrise or sunset. When it is possible to observe this bar, the changes in its position
at intervals of a few hours will enable the observer to determine the direction of
movement of the storm.
481. CHARACTER OF TROPICAL CYCLONIC STORMS. Within the tropics the
storm area is small, the region covered by violent winds extending in general not
more than 150 miles from the center. The barometric gradients are, however,
exceedingly steep, instances having been recorded in which the difference of pressure
fPorto St."
IN LOW LATITUDES
Velocity along pafh
about 11 miles per tour
20
80
70
FIG. 73.
CYCLONIC STORMS.
219
for this distance amounted to 2 inches. In the typhoons of the Xorth Pacific Ocean
gradients of one inch in 60 miles are not infrequent. The successive isobars are
almost circular. As a consequence of this distribution of pressure the winds on the
slopes of the depression are frequently of great violence, and in the matter of direc-
tion they are more sym-
I j i i i i i i i i i i i i i i i i i i i = QO metrically disposed about
the center than is the
case with the larger and
less regularly shaped de
pressions of higher lati
tudes. In these low lati
tudes the average values
of the deflection of the
wind from the baromet
ric gradient is in the
neighborhood of six cpm-
10 pass points to the right
in the northern hemi
sphere, to the left in the
southern.
482. To Fix THE
BEARING OF THE STORM
CENTER FROM THE VES
SEL. On this assump
tion, the following rules
will enable an observer
to fix the bearing of the
20 storm center from his
vessel:
In the northern hem
isphere, stand with the
face to the wind; the
storm center will bear ten
points to the observer s
right.
In the southern hem
isphere, stand with the
face to the wind; the
storm center will bear ten
30 points to the observer s
left.
On the basis of these
rules the tables hereafter
given (art. 487) show the
bearing of the center
corresponding to a wind
FlQ - 74 - of any direction.
483. To Fix THE DISTANCE OF THE STORM CENTER FROM "THE VESSEL. The
following table, taken from Piddington s " Sailor s Horn Book/ may prove of some
assistance in estimating the distance of the storm center from the vessel:
Average fall of the barometer
per hour.
From 0. 02 to 0. 06 in.
From 0. 06 to 0. 08 in.
From 0. 08 to 0. 12 in.
From 0. 12 to 0. 15 in.
Distance from the storm
center.
From 250 to 150 miles.
From 150 to 100 miles.
From 100 to 80 miles.
From 80 to 50 miles.
The table assumes that the vessel is hove-to in front of the storm and that the
latter is advancing directly toward it.
220 CYCLONIC STORMS.
Inasmuch, as cyclones are of varying area and of different intensities, the lines of
equal barometric pressure (isobars) lie much closer together in some storms than in
others, so that, in the circumstances of an observer on the ocean, the estimation of
the distance of the center by the height of the mercurial column or of its rate of fall
must be somewhat conjectural.
484. To AVOID THE CENTER OF THE STORM. In the immediate neighborhood
of the center itself the winds attain full hurricane force, the sea is exceedingly
turbulent, and there is danger of being taken aback. Every effort should therefore
be made to avoid this region, either by running or by heaving-to; and if recourse is
had to the latter maneuver, much depends upon the selection of the proper tack;
this being in every case the tack which will cause the wind to draw aft with each
successive shift.
A vessel hove-to in advance of a tropical cyclonic storm will experience a long
heavy swell, a falling barometer with torrents of rain, and winds of steadily increasing
force. The shifts of wind will depend upon the position of the vessel with respect
to the path followed by the storm center. Immediately upon the path, the wind
will hold steady in direction until the passage of the central calm, trie "eye of the
storm," after which the gale will renew itself, but from a direction opposite to that
which it previously had. To the right of the path, or in the right-hand semicircle
of the storm (the observer being supposed to face along the track), the wind, as the
center advances and passes the vessel, will constantly shift to the right, the rate at
which the successive shifts follow each other increasing with the proximity to the
center; in this semicircle, then, in order that the wind shall draw aft with each
shift, the vessel must be hove-to on the starboard tack; similarly, in the left-hand
semicircle, the wind will constantly shift to the left, and here the vessel must be
hove-to on the port tack.
These rules hold alike for both hemispheres and for cyclonic storms in all
latitudes.
Figure 75 represents a cyclonic storm in the northern hemisphere after recurving.
For simplicity the area of low barometer is made perfectly circular, and the center is
assumed to be ten points to the right of the direction of the wind at all points within
the disturbed area. Let us assume that the center is advancing about NNE., in the
direction of the long arrow, shown in heavy full line. The ship a has the wind at
ENE.; t she is to the left of the track, or technically in the navigable semicircle.
The ship b has the wind at ESE. and is in the dangerous semicircle. As the storm
advances these ships, if lying to, a upon the port tack, b upon the starboard tack, as
shown, take with regard to the storm center the successive positions a, a 1} etc., b, 6 1 ,
etc., the wind of ship a shifting to the left, of ship b to the right, or in both cases
drawing aft, and thus diminishing the probability of either ship being taken aback,
a danger to which a vessel lying to on the opposite tack (i. e., the starboard tack in
the left-hand semicircle or the port tack in the right-hand semicircle) is constantly
exposed, the wind in the latter case tending constantly to draw forward. The ship b
is continually beaten by wind and sea toward the storm track. The ship a is drifted
away from the track, and, should she be able to carry sail, would soon find better
weather by running off to the westward.
It must not be forgotten that the shifts of wind will only occur in the above order
when the vessel is stationary. When the course and speed are such as to maintain
a constant relative bearing between the ship and storm center, there will be no shift
of wind. jShould the vessel be outrunning the storm, the wind will indeed shift in
the opposite direction to that given, and a navigator in the right semicircle, for
instance, and judging only by the shifts of wind without taking into account his own
run, might imagine himself on the opposite side. In such a case the barometer must
be the guide.
An examination of figure 75 shows how this is. A vessel hove to at the position
marked 6, and being passed by the storm center, will occupy successive positions in
regard to the center from b to 6 4 , and will experience shifts of wind, as shown by the
arrows^ from East through South to SW. On the other hand, if the storm center
be stationary or moving slowly and a vessel be overtaking it along the line from 6 4
to Z>, the wind will back from SW. to East, and is likely to convey an entirely wrong
impression as to the location and movement of the center.
CYCLONIC STOBMS.
221
485. DANGEROUS AND NAVIGABLE SEMICIRCLES. Prior to recurving, the winds
in that semicircle of the storm which is more remote from the equator (the right-
hand semicircle in the northern hemisphere, the left-hand semicircle in the southern)
are liable to be more severe than those of the opposite semicircle. A vessel hove to
in the semicircle adjacent to the equator has also the advantage of immunity from
becoming involved in the actual center itself, inasmuch as there is a distinct tendency
on the part of the latter to move away from the equator. For these reasons the more
remote semicircle has been called the dangerous, the less remote the navigable.
486. MANEUVERING. A vessel suspecting the dangerous proximity of a tropical
cyclonic storm should lie-to for a time on the starboard tack to locate the center by
observing shifts of the wind and the behavior of the barometer. If the former holds
H
steady and increases in force, while the latter falls rapidly, say at a greater rate than
0.03 of an inch per hour, the vessel is probably on the track of the storm and in advance
of the center. In this position the proper step (providing, of course, that sea room
permits) is to run, keeping the wind, in the northern hemisphere, at all times well on
the starboard quarter; in the southern hemisphere, well on the port; and thus
constantly increasing the distance to the storm center. The same rule holds good
if the observation places the vessel at but a scant distance within the forward quadrant
of the dangerous semicircle. Here, too, the natural course will be to seek the navigable
semicircle of the storm, even though such a course involves crossing the track in
advance of the center, always exercising due caution to keep the wind from drawing
too far aft.
222 CYCLONIC STORMS.
The critical case is that of a vessel which finds herself in the forward quadrant
of the dangerous semicircle and at a considerable distance from the track, for here
the shifts of the wind are sluggish and the indications of the barometer are undecided,
both causes conspiring to render the bearing of the center doubtful. If, upon
heaving to, the barometer becomes stationary, the position should be maintained
until indications of a rise are apparent, upon which the course may be resumed with
safety and held as long as the rise continues. If, however, the barometer falls, a
steamer should make a run to the NNE. or NE. (southern hemisphere, SSE. or SE.),
keeping the wind and sea a little on the port (southern hemisphere, starboard) bow,
and using such speed as will at least keep the barometer stationary. Such a step will
in general be attended with the assurance that the present weather conditions will
in any case grow no worse. For a sailing vessel, unable to stand closer to the wind
than six points, the last maneuver will be impossible, and driven to leeward by wind,
sea, and current, she may be compelled to cross the track immediately in advance
of the center, or may even become involved in the center itself. In this extremity
the path of the storm center during the past twenty-four hours should be laid down
on a diagram as accurately as the observations permit, and the line prolonged for
some distance beyond the present position of the center. Having assumed an average
rate of progress for the center, its probable position on the line should be frequently
and carefully plotted, and the handling of the vessel should be in accordance with
the diagram.
487. SUMMARY OF RULES. The following summary comprises the rules of
maneuvering, so far as they may be made general:
NORTHERN HEMISPHERE.
In the Right or Dangerous Semicircle. Steamers bring the wind on the starboard
bow, and make as much way as possible; if obliged to heave to, do so head to sea.
Sailing vessels haul by the wind on the starboard tack and carry sail as long as possible ;
if obliged to heave to, do so on the starboard tack.
In the Left or Navigable Semicircle. Bring the wind on the starboard quarter,
note the course, and hold it; if obliged to heave to, do so on the port tack, unless in
a steamer which behaves better when hove to stern to the sea.
On the Storm Track in Front of the Center. Bring the wind two points on the
starboard quarter, and, holding this course, run for the Left Semicircle; if obliged
to heave to, do so on the port tack, unless in a steamer which behaves better when
hove to stern to the sea.
On the Storm Track in Rear of the Center. Avoid the center by the best
practicable route, having due regard to the tendency of cyclones to recurve to the
northward and eastward.
SOUTHERN HEMISPHERE.
In the Left or Dangerous Semicircle. Steamers bring the wind on the port bow,
and make as much way as possible; if obliged to heave to, do so head to sea. Sailing
vessels haul by the wind on the port tack, and carry sail as long as possible; if obliged
to heave to, do so on the port tack.
In the Right or Navigable Semicircle. Bring the wind on the port quarter, note
the course, and hold it; if obliged to heave to, do so on the starboard tack, unless in
a steamer which behaves better when hove to stern to the sea.
On the Storm Track in Front of the Center. Bring the wind two points on the
port quarter, and, holding this course, run for the right semicircle; if obliged to
heave to, do so on the starboard tack, unless in a steamer which behaves better when
hove to stern to the sea.
On the Storm Track in Rear of the Center. Avoid the center by the best practi
cable route, having due regard to the tendency of cyclones to recurve to the south
ward and eastward.
CYCLONIC STORMS.
223
The application of these rules for the various directions of the wind is shown
in the following table:
Storm Table, Xorthern Hemisphere.
Direction
of wind.
Direction
of center.
Observer facing along storm track.
If wind shifts toward If wind shifts toward If wind stead v with
the right. the left. falling barometer.
If wind steady with
rising barometer.
North.
ESE.
g> R un SSW. = Run SSW.
Run SSW. ~
XXE.
SE.
rr.^~9-- -
Run SW. "g Kg.
Run SW. ^ . =-
Run SW. 5- -: -
XE.
SSE.
~K 1= * ^L\~
Run WSW. ZL . 7"
Run WSW. ?.^r
Run WSW. 5 - ~
EXE. ! South.
-, S^S-SBS
Run West, r r: =
Run West. g ~ c
Run West, o ^ f
East.
SSW.
? 8 liffjTg.5.
Run WNW. i.^ =
Run WXW. 1-^
Run WNW. a 1 ! 5
ESE.
SW.
M3&Rg
Run N W. - *
RunNW. - c-~
RunNW. ^-^
SE.
wsw. .
X ^ X ^ /* ^ JQ
RunXXW. s
RunXXW. ^
RunXXW. S b
SSE.
West.
5 Sfc* ~ X- ^
5 o* *** 3 4
Run North. ~ Z
Run North. 9
Run North. r~5
South.
WNW.
~P-P;F^-- RunXXE. 0-
RunXXE. < =
RunXXE. g -
SSW.
NW.
fcs.e- i*.
Run XE. < =
Run XE.
RunXE. ^|
sw.
NNW.
5. ** 2 5! c* =
Run EXE. #J
Run EXE. ~
Run EXE. ~^:.
wsw.
North.
*.S X ^;
Run East. - *
Run East. e ~
Run East. - m
West.
NNE.
RsH* iT-
Run ESE. 9-~
Run ESE. ~\
Run ESE. ^
WXW.
NE.
5:1 si" M- RSE. ;i
RunSE. -T- ^
RunSE.
NW.
ENE.
, _~~ c^c j RimSSE .
Run SSE. 5
Run SSE.
NNW.
East.
** Pg 3- Run South. g ~
Run South. jx;
Run South. Jf
Courses given are for wind two points on starboard quarter, but it is preferable to take wind broad on quarter if possible.
Storm Table, Southern Hemisphere.
Direction
of wind.
Direction
of center.
Observer facing along storm track.
If wind shifts toward
the right.
If wind shifts toward
the left.
If wind steady with
falling barometer.
If wind steady with
rising barometer.
North.
WSW.
Run SSE. ~
2P 2
Run SSE. ~
Run SSE. ~
XXE.
West.
Run South. ^ -
9- S "z r" El ^ ^
Run South. ^ - 2-
Run South. *3 s; -
XE.
WNW.
Run SSW. 1 x. ~
a ~ 2- = s P. H- 3
Run SSW. E.^7
Run SSW. i.-
EXE.
NW T .
RunSW. c^r.6
c ? : ^ < ? ^ = i
RunSW. 3 J ^ =
RunSW. ^=:d
East.
XXW.
Run WSW. 5*51
Run WSW. 5 -
Run WSW. J. 7 ^ 5
ESE.
North.
Run West. ~~-
^ e-T- x ^ r: ~ 5.
Run West. HT""
Run West. ~o
SE.
NNE.
Run WNW. % g-
. ^- S r " J ^ 5c -p
Run WNW. S ^g
Run WXW. S" a
SSE.
NE.
RunNW. F~Z
- - ~ = 1
RunXW. f^j? r-
RunXW. -2
South.
ENE.
Run NNW. 5 r
^ ?.H S" = r-
RunNNW. < =
Run NNW. r-
SSW.
East.
Run North. ~ =
p 35 5 cf ?" 2-
Run North.
Run Xorth. ^ 3
SW.
ESE.
Run NNE. ^ V!
(L-< -- p ^ c
Run XXE. ^ =
Run XXE. g^J
WSW.
SE.
RunXE.
c" | x ex" 2
RunXE. cJS
RunNE.
West,
SSE.
Run EXE. -x
5**^J| ?" g "5
Run ENE. c|
Run EXE. --5
WXW.
South.
Run East. ^
^ x =" ~ _* c?-
Run East. 2 ^
Run East. ^ : i
NW.
SSW.
Run ESE.
S t^Pi C- - _-
C C - x X
Run ESE.
Run ESE.
NNW.
SW.
Run SE. Jf
.= 51 ifi
RunSE. -
Run SE. $
a Courses given are for wind two points on port quarter, but it is preferable to take wind broad on quarter if possible.
488. EXTRA-TROPICAL CYCLONIC STORMS. On turning to the cyclones of tem
perate latitudes, we find many features in which they resemhle those of the torrid
zone, but certain other features in which they differ. Their fundamental resemblance
to tropical cyclones is seen in their incurving winds, forming an inflowing left-handed
spiral about the center of low pressure in the northern hemisphere, an inflowing right-
handed spiral in the southern. The intensity of these winds varies with the depth of
the barometric depression. The depression itself, however, in place of covering a few
miles, as is the case in the tropics, will frequently have a diameter of several hundred
or even a thousand miles, and for some distance around the center the gradients will
have a tolerably strong value. For this reason there is less concentration of violence
close to the center, and the calm and clear central space, or "eye," is seldom sharply
developed, although it is not uncommon to discover a gradual weakening or failing
224
CYCLONIC STORMS.
of the winds, and sometimes even an imperfect breaking^ away of the clouds as the
central area passes over the observer. The form of tropical cyclones as denned by
their isobaric lines is nearly circular. Extra-tropical cyclones are as a rule less
symmetrical, and their isobars are often elongated into an oval form, the longer axis
of the oval trending (in the northern hemisphere) between north and east about,
therefore, in the direction of progression. The steepest gradients, and consequently
die strongest winds, are apt to be found on the equatorial and westerly sides of the
depression.
Extra-tropical cyclones generally follow an easterly course, inclining somewhat
toward the pole; but they occasionally turn to one side or the other, become sta
tionary, or even move backward. The velocity of progression varies from 15 to 40
miles an hour. If they exist as independent barometric depressions, with strong
upward gradients on all sides of the center, the cyclonic circulation will be complete,
the wind shifting with the sun for an observer situated in the equatorial semicircle
of the storm, against the sun for an observer situated in the polar semicircle.
Important among these extra-tropical cyclonic disturbances are the pamperos
of the Argentine coast. These storms are primarily caused by the approach and
passage eastward of an area of low pressure, around which the winds circulate spirally
in a right-handed direction. They vary in strength and duration from a squall to a
gale of great violence. Although preceded by the indications which characterize
the approach of cyclonic storms in general, yet they usually break with such sudden
ness, in a shift of wind from the northward to the southwestward, that they may
become particularly dangerous from this cause alone. They usually continue to
blow and die out in the southwest quadrant.
489. STORMS ALONG THE TRANSATLANTIC STEAMSHIP ROUTES. The storms
which are so frequently met during the winter season along the steamship routes
between America and Europe are not, as a rule, due to central barometric depressions
but to depressions having a trough or V shape, which extend southerly from the
extensive permanent area of low pressure having its center in the vicinity of Iceland.
They are not attended by complete
cyclonic circulations, inasmuch as
the polar gradients which would
otherwise give rise to easterly winds
on this polar side are lacking. Their
approach is heralded by a gradual
hauling of the wind to southward,
which is later followed (at the time
of passage of the central line of the
trough) by a change to NW., accom
panied by heavy rain squalls and a
rapid increase in force. The general
distribution of pressure and the sur
rounding winds are ^ shown in figure 76. The changes in wind and pressure ensue
much more rapidly in the case of a westward-bound vessel than in that of one east
ward bound, the rate at which the observer and the depression approach each other
being^ in the former case the sum of his own westward velocity and the eastward
velocity of the trough, in the latter case the difference of these velocities.
Low
FIG. 76.
CHAPTER XX.
TIDES,
490. DEFINITIONS. Tidal phenomena present themselves to the observer
under two aspects as alternate elevations and depressions of the sea, and as recur
rent inflows and outflows of streams. The word tide, in common and general usage,
is made to refer without distinction to both the vertical and horizontal motions of
the sea, and confusion has sometimes arisen from this double application of the term;
in its strict sense, this word may be used only with reference to the changes of eleva
tion, while the recurrent streams are properly distinguished as tidal currents.
The tide rises until it reaches a maximum height called high water or high tide,
and then falls to a minimum level called law water or low tide; that period at high or
low water marking the transition between the tides, during which no vertical change
can be detected, is called stand.
Of the tidal currents, that which arises from a movement of the water in a
direction, generally speaking, from the sea toward the land, is called flood, and that
arising from an opposite movement, ebb; the intermediate period between the cur
rents, during which there is no horizontal motion, is distinguished as slack. Set and
drift are terms applicable to the tidal currents, the first referring to the direction and
the second to the velocity.
Care should be taken to avoid confusing the terms relating to tides with those
which relate to tidal currents.
491. CAUSE. The cause of the tides is the periodic disturbance of the ocean
from its position of equilibrium brought about through the periodic differences of
attraction upon the water particles of the earth, by the moon, and to lesser degree,
by the sun, on account of their relative periodic movements. The tide-producing
force of the moon upon a particle of unit mass on the surface of the earth is the
difference between the moon s attraction upon the given unit mass and the moon s
attraction upon the entire earth; and it is likewise with the sun, only the magnitude
of the mean tide-producing force is in this case reduced to about two-fifths of the
tide-producing force of the moon, because of the comparative remoteness of the sun
from the earth.
A particle which has a tide-producing body in its zenith or in its nadir experi
ences, as the result of the attraction of the tide-producing body, an effect only in the
vertical direction as il the intensity of gravity were momentarily lessened; and a
particle which has the tide-producing body in its horizon, being then practically at
the same distance from the tide-producing body as the center of the earth, experi
ences, as the result of the attraction of the tide-producing body, an effect which is
practically ah 1 in the vertical direction as if the intensity of gravity w T ere momentarily
increased. But when the tide-producing body is in any other situation withreference
to an attracted particle, the attraction is partly" directed in a vertical line toward the
center of the earth and partly in a horizontal direction along the surface of the earth.
The vertical components of the attractions of the tide-producing bodies can not
create any sensible disturbance on the existing oceans; but the horizontal components
of such attractions, tending to produce horizontal movements oscillating back and
forth on the surface of the earth, are effective in the production of the tides, and, by
acting upon portions of the oceans that are susceptible of taking up stationary
oscillations in approximate unison with the period of the tide-producing forces, give
rise to the dominant tides.
The peculiarities that characterize the tides of many localities are caused by
modifications resulting from reflections and interferences suffered by the dependent
waves generated by the dominant tides. Theory is not yet sufficiently advanced to
render practicable the prediction of the tides where no observations have been made;
61828 16 15 225
226 TIDES.
but by theory, supplemented by the observation of actual tidal conditions in a given
locality during a certain period of time, very accurate predictions of the time and
height of the tides can be mado for that locality.
492. ESTABLISHMENT. High and low water occur, on the average of the twenty-
eight days comprising a lunar month, at about the same intervals after the transit
of the moon over the meridian. These nearly constant intervals, expressed in hours
and minutes, are known, respectively, as the high water lunitidal interval and low
water lunitidal interval.
The interval between the moon s meridian passage at any place and the time
of the next succeeding high water, as observed on the days when the moon is at full
or change, is called the vulgar (or common) establishment of that place, or, sometimes,
simply the establishment. This interval is frequently spoken of as the time of high
water on full and change days (abbreviated "H. W. F. & C."); for since, on such
days, the moon s two transits (upper and lower) over the meridian occur about
midnight and noon, the vulgar establishment then corresponds closely with the local
times of high water. When more extended observations have been made, the average
of all high water lunitidal intervals for at least a lunar month is taken to obtain what
is termed, in distinction to the vulgar establishment, the corrected establishment of
the port, or mean high water lunitidal interval. In defining the tidal characteristics
of a place some authorities give the corrected establishment, and others the vulgar
establishment, or "high water, full, and change;" calculations based upon the former
will more accurately represent average conditions, though the two intervals seldom
differ by a large amount.
Having determined the time of high water by applying the establishment to the
time of moon s transit, the navigator may obtain the time of low water with a fair
degree of approximation by adding or subtracting 6 h 13 m (one-fourth of a mean lunar
day) ; but a closer result will be given by applying to the time of transit the mean
low water lunitidal interval, which occupies the same relation to the time of low water
as the mean high water lunitidal interval, or corrected establishment, does to the
time of high water.
493. KANGE. The range of the tide is the difference in height between low
water and high water. This term is often applied to the difference existing under
average conditions, and may in such a case be designated as the mean range or mean
rise and fall to distinguish it from the spring range or neap range, winch are the ranges
at spring and neap tides, respectively.
494. SPRING AND NEAP TIDES. At the times of new and full moon the relative
positions of sun and moon are such that the high water produced by one of those
bodies occurs at the same time as that produced by the other, and so also with the
low waters; the tides then occurring, called spring tides, have a greater range than
any others of the lunar month, and at such times the highest high tides as well as
the lowest low tides are experienced, the tidal range being then at its maximum.
At the first and third quarters of the moon the positions are such that the high tide
due to one body occurs at the time of the low tide due to the other, so that the two
actions are opposed ; this causes the neap tides, which are those of minimum range,
the high waters being lower and the low waters higher than at other periods of the
month.
Since the horizontal motion of the water depends directly upon the rise and fall
of the tides it follows that the currents will be greatest at springs and least at neaps.
The effect of the moon s being at full or change is not felt at once in all parts of the
world, and the greatest range of tides does not generally occur until one or two days
thereafter; thus, on the Atlantic coast of North America, the highest tides are
experienced one day, and on the Atlantic coast of Europe two days, afterwards,
though on the Pacific coast of North America they occur nearly at full and change.
495. The nearer the moon is to the earth the stronger is its attraction, and as
it is nearest in perigee, the tides will be larger then on that account, and consequently
less in apogee. For a like reason, the tides will be increased by the sun s action when
the earth is near its perihelion, about the 1st of January, and decreased when near
its aphelion, about the 1st of July.
496. The height of the tides at any place may undergo modification on account
of strong prevailing winds or abnormal barometric conditions, a wind blowing off
TIDES.
227
the shore or a high barometric tending to reduce the tides, and the reverse. The
effect of atmospheric pressure is to create a difference of about 2 inches in the height
of tide for every tenth of an inch of difference in the barometer.
497. PRIMING AND LAGGING. The tidal day is the variable interval, averaging
24 h 50 m , between two alternate high or low waters. The amount by which corre
sponding tides grow later day by day that is, the amount by whicli the tidal day
exceeds 24 h is called the daily retardation. When the sun s tidal effect is such as to
shorten the lunitidal intervals, thus reducing the length of the tidal day and causing
the tides to occur earlier than usual, there is said to be ^priming of the tide; when,
from similar causes, the interval is lengthened, there is saia to be a lagging.
498. TYPES OF TIDES. The observed tide is not a simple wave ; it is a compound
of several elementary undulations, rising and falling from the same common plane,
of which two can be distinguished and separated by a simple grouping of the
data. These two waves are known as the semidiurnal and the diurnal tides, be
cause the first, if alone, would give two high and two low waters in a day, while
the second would give but one high and one low water in an equivalent period
of time. In nearly all ports these two tides coexist, but the proportion between
them varies remarkably for differ
ent seas. The effect of the com
bination of these two types of
tide is to produce a "diurnal
inequality, both in the height of
two consecutive high or low
waters, and in the intervals of
time between then" occurrence.
The height of the diurnal wave
may be regarded as reaching a
maximum fortnightly, soon after
the moon attains its extreme dec
lination and is therefore near
one of the tropics. The tides
that then occur are denominated
tropic tides.
In undertaking to investi
gate the tides of a port it is im
portant to ascertain as early as
possible the form of the tide ; that
is, whether it resembles the semi
diurnal, the diurnal, or the mixed
tvpe; because not only may this information be of scientific value, but the knowledge
tnus gained at the outset will enable the observer to fix upon the best method of
keeping his record.
499. The type forms referred to are illustrated in the diagram in figure 77,
where the waves are plotted in curves, using the times as abscissas and the heights
as ordinates. In this diagram, the curve traced in the full line is a tide wave of the
semidiurnal type; that traced by the dotted line one of the diurnal; while the
broken line is one of the mixed type, in this case the compound of the two others.
In order to determine the type to which the tide of any port belongs, it is usually
only necessary to make hourly observations for a day or two at the date of the moon s
maximum declination, and to repeat the series about a week later, when the moon
crosses the equator. The reported irregularities of the rise and fall at any place
should not deter persons from careful investigation. When analyzed, even the most
complicated of tides are found to follow some general law.
500. TIDAL CURRENTS. It should be clearly borne in mind by the navigator
that the periods of flood and ebb currents do not necessarily coincide with those of
rising and falling tides, and that, paradoxical though it may seem at first thought,
the inward set of the surface current does not always cease when the water nas
attained its maximum height, nor the outward set when a minimum height has been
reached. Under some circumstances it may occur that stand and slack will be
(
) 1
:
1
* .
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Semidiurnal.
diurnal.
FIG. 77.
mixed.
228 TIDES.
simultaneous, while other conditions may produce a maximum current at stand,
with a maximum rate of rise or fall at slack water.
The varying effects which will be produced according to local conditions may
be considered by the comparison of two tidal basins, to one of which the tide wave
has access from the sea by a channel of ample capacity, while the other has an
entrance that is narrow and constricted. In the first case, the process of filling or
emptying the basin keeps pace with the change of level in the sea and is practically
completed as soon as the height without becomes stationary; in this case slack and
stand occur nearly at the same time, as do flood and rise and ebb and fall. In the
second case, the limited capacity of the entrance will not permit the basin to fill or
empty as rapidly as the tide changes its level without; hence there is still a difference
of level to produce a current when the vertical motion in either direction has ceased
on the outside, and for a considerable time after motion in the reverse direction has
been in progress; under extreme conditions it may even occur that a common level
will not be established until mid-tide, and therefore the surface current at some
places will ebb until three hours after low water and flow until three hours after high
water.
Localities that partake of the nature of the first case are those upon open coasts
and wide-mouthed bights. Examples of the latter class will be found in narrow
bays and long channels.
TIMES OF HIGH AND LOW WATER.
501. TIDE TABLES. The most expeditious, as well as most exact, method of
ascertaining the times of high and low water and other features of the tides will be
by reference to a Tide Table, and every navigator is recommended to provide him
self with such a publication. The United States Coast and Geodetic Survey pub
lishes annually, in advance, tables giving, for every day in the year, the predicted
time and height of the tides at certain principal ports of the world, and from these,
by a simple reduction, the times and lieights at a multitude of other ports may
readily be obtained; data for ascertaining the tidal currents in certain important
regions are also provided. General tide tables are also published by the govern
ments of other maritime nations, and special tables are to be had for many particular
localities.
502. Where no tide tables are available, the method of calculation by applying
the lunitidal interval to the time of the moon s meridian passage must be resorted to.
To do this, find first the time of the moon s meridian passage, upper or lower,
as may be required. The Greenwich mean time of upper transit at Greenwich is
given in the Nautical Almanac; the corresponding time of lower transit is most easily
found by taking the mean of the two adjacent upper transits; to the Greenwich time
of Greenwich transit apply the correction for longitude given in Table 1 1 (using the
daily variation of the moon s meridian passage shown in the Almanac), adding in
west and subtracting in east longitude ; the result is the local mean time of local
transit. Add to this the high-water or low- water lunitidal interval of the port from
Appendix IV, according as the time of high or low water may be required. The
result is the time sought.
The astronomical date must be strictly adhered to, and in so doing it may be
found necessary to employ the time of a lower transit, or the transit of a preceding
day, to find the time of the tide in question.
Appendix IV contains, besides the geographical positions of all the more
important positions in the world, a series of tidal data relating to many of those
places. In such data are comprised the mean lunitidal intervals for high and low
water; also, for places where the semi-diurnal type of tide prevails, the tidal range
at spring and at neap tides, and for those where the tide is of the diurnal type, tjie
tropic range. An alphabetical index is appended to this table.
The corrected establishment taken from the charts may be substituted for the
high-water lunitidal interval of the table; or, with only slight variation in the results,
the vulgar establishment (H. W. F. & C.) may be employed.
TIDES. 229
EXAMPLE: Find the times of the high and low waters at the New York Navy Yard, occurring next
after noon on April 15, 1916.
G.M. T. of Gr. upper transit, 14<i 9^21 Transit (lower), 14<* 21 52 Transit (lower), 14<* 21> 52
G. M. T. of Gr. upper transit, 15 10 05 H. W.Lun.Inf.(App.IV), 8 44 L. W.Lun.Int.(App.IV), 2 49
2)29 19 26 f 15 6 36 f 15 41
L.M.T..H.W., -L\pr.lo.6.36 L.M.T..L.W., {Apr. 15,12.41
G.M. T. of Gr. lower transit 14 21 43 I p.m. I p.m.
Corr. for -f 74 Long. (Tab. 11), + 9
L. M. T. of local lower transit 14 21 52
EXAMPLE: Find the time of high water at the Presidio, San Francisco, Cal., on the evening of
February 17, 1916.
G. M. T. of Gr. upper transit, 16<i 10 h 37
G. M. T. of Gr. upper transit, 17 11 23
2)33 22 00
G. M. T. of Gr. lower transit,
Corr. + 122 Long. (Tab .11;,
L. M. T. local lower transit,
H. W. Lun. Int. (App. IV),
L. M. T., H. W. f
EXAMPLE: Find the time of low water at Singapore on the night of May 21, 1916.
G. M. T. of Gr. upper transit, 20<i 15*> 29
G. M. T. of Gr. upper transit, 21 16 28
2)42 7 57
G. M. T. of Gr. lower transit, 21 3 59
Corr. for -104 Long. (Tab. 11), 17
L. M. T. of local lower transit, 21 3 42
L. W. Lun. Int. (App. IV) + 4 02
T \r T T \v / 21 7 **
L. M. !.,!>. \N., \May21, 7.44 p. m.
EXAMPLE: Find the time of morning hish water and afternoon low water at Gibialtar on June 19,
1916.
G. M. T. of Gr. upoer transit, 18<* 15* 12 G. M. T. of Gr. upper transit,
Corr. -f-5 Long. (Tab. 11), + 01 G. M. T. of Gr. upper transit,
L. M. T. of local transit, 18 15 13 2)38 7 17
H. W. Lun. Int. (App. IV), 1 35
G. M. T. of Gr. lower transit, 19 3 39
T \r T TT w 118 16 48 Corr. for +5 Long. (Tab. 11), -f 01
L. M. T., H. W., | June 19j 4 4g a m ^
L. M. T. of local lower transit, 19 3 40
L. W. Lun. Int. (App. IV), 7 55
T \r T w / 19 11 35
I* M. T. t 1* W., \June 19, 11.35 p.m.
TIDAL OBSERVATIONS.
503. Since navigators will frequently have opportunity to observe tidal con-
, ditions, either in connection with a hydrographic survey or otherwise, at places
where existing knowledge of the tides is incomplete, an understanding of the methods
employed in tidal observations may be important.
50i . TIDES. For the proper study of tides, frequent and continuous observa
tions are necessary; it will not suffice to observe the heights of the high and low
waters only, even if they present themselves as distinct phases, but the whole tidal
curve for each day should be developed by recording the height of water at intervals,
which, preferably, should not exceed thirty minutes. Observations, to be complete,
* must cover a whole lunar month; or, if it be impracticable to observe the tides at
night, the day tides of two lunar months may be substituted.
505 . When made for the purposes of a hydrographic survey, the tidal observations
are used to correct the soundings, and care must be taken to make sure that the
gauge is placed in a situation visited by the same form of tide as that which occurs
at the place where soundings are being made. It will not answer, for instance, to
230 TIDES.
correct the soundings upon an inlet bar by tidal observations made within the lagoon
with which this inlet communicates, because the range of the tide within the lagoon
is less than upon the outside coast. A partial obstruction, like a bridge, or a natural
contraction of the channel section, while it may not reduce the total range of the tide
or materially affect the time of high or low tides, will alter the relative heights above
and below at intermediate stages, so that the hydrographer must be careful to see
that no such obstruction intervenes between his field of work and the gauge.
506. TIDAL CURRENTS. Observations for tidal currents should be made with
the same regularity as for tides; the intervals need not ordinarily be more frequent
than once in every half hour. They should always be made at the same point or
points, which should be far enough from shore to be representative of the conditions
prevailing in the navigable waters. The ordinary log may be employed for measuring
the current, but it is better to replace the chip by a pole weighted to float upright
at a depth of about fifteen feet; the line should be a very light one, and buoyed at
intervals by cork floats to keep it from sinking; the set of the current should be
noted by a compass bearing of the direction of the pole at the end of the observation.
507. RECORD. The record of observations should be kept clearly and in
complete form. It should include a description of the locality of observation, the
nature of gauge and of instruments used for measuring currents, and the exact position
of both tidal and current stations, together with situation and height of bench mark.
The time of making each observation should be shown, and data given for reduction
to some standard time. In extended tidal observations the meteorological conditions
should be carefully recorded, the instruments used for the observations being properly
compared with standards.
508. There are frequently remarkable facts in reference to tides and currents
to be obtained from persons having local knowledge; these should be examined and
recorded. The date and circumstances of the highest and lowest tides ever known
form important items of information.
509. PLANES OF REFERENCE. The plane of reference is the plane to which
soundings and tidal data are referred. One of the principal objects of observing
tides when making a survey is to furnish the means for reducing the soundings to
this plane. Four planes of reference are used; namely, mean low water, mean low
water springs, mean lower low Waters, and the harmonic or Indian tide plane.
Mean Low water is a plane whose depression below mean sea level corresponds
with half the mean semidiurnal range, while the depression of mean low water springs
corresponds with half the mean range of spring tide; mean lower low water depends
upon the diurnal inequality in high and low water; the harmonic or Indian tide plane
was adopted as a convenient means of expressing something of an approximation
to the level of low water of ordinary spring tides, but where there is a large diurnal
inequality in low waters it falls considerably below the true mean of such tides.
As these planes may differ considerably, it is important to ascertain which plane
of reference is adopted before making use of any chart or considering data concerning
the tides.
510. The tides are subject to so many variations dependent upon the movements
of the sun and moon, and to so many irregularities due to the action of winds and
river outflows, that a very long series of observations would be necessary to fix any
natural plane. In consideration of this, and keeping in view the possibilities of
repetitions of the surveys or subsequent discoveries within the field of work, it is
necessary to define the position of the plane of reference which has resulted from any
series of observations. This is done by leveling from the tide gauge to a permanent
bench, precisely as if the adopted plane were arbitrary.
511. BENCH MARK. The plinth of a lighthouse, the water table of a substantial
building, the base of a monument, and the like, are proper benches; and when these
are not within reach a mark may be made on a rock not likely to be moved or started
by the frost, or, if no rock naturally exists in the neighborhood, a block of stone
buried below the reach of frost and plowshare should be the resort. When a bench
is made on shore it should be marked by a circle of 2 or 3 inches diameter with a
cross in the center indicating the reference point. The levelings between this point
and the gauge should be run over twice and the details recorded. A bench made
upon a wharf or other perishable structure is of little value, but in the absence of
TIDES. . 231
permanent objects it is better than nothing. The marks should be cut in, if on stone,
and if on wood, copper nails should be used. The bench must be sketched and
carefully described, and its location marked on the hydrographic sheet, with a state
ment of the relative position of the plane of reference.
512. The leveling from the bench mark to the tide gauge may be done, when a
leveling instrument is not available, by measuring the difference of height of a number
of intermediate points by means of a long straight-edged board, held horizontal by
the aid of a carpenter s spirit level, or even a plummet square, taking care to repeat
each step with the level inverted end for end. A line of sight to the sea horizon,
when it can be seen from the bench across the tide staff, will afford a level line of
sufficient accuracy, especially when observed with the telescope. It may often be
convenient to combine these methods.
513. TIDE GAUGES. The Staff Gauge is the simplest device for measuring the
heights of tides, and in perfectly sheltered localities it is the best. It consists of a
vertical staff graduated upward in feet and tenths, and so placed that its zero shall
lie below the lowest tides. The same gauge may also be used where the surface is
rough, if a glass tube with a float inside is secured alongside of the staff, care being
taken to practically close the lower end of the tube so as to exclude undulations;
readings may also be made by noting the point midway between the crest and trough
of the waves.
A staff gauge should always be erected for careful tidal observations, even where
other classes of gauge are to be employed, as it furnishes a standard for comparison
of absolute heights, and also serves to detect any defects in the mechanical details
upon which all other gauges are to a greater or less extent dependent.
514. Where there is considerable swell, and where, from the situation of the
gauge or the great range of the tide (making it inconvenient for the observer to see
the figures in certain positions) the staff gauge can not be used, recourse must be had
to the Box Gauge. This gauge consists of a vertical box, closed at the bottom, with
a few small holes in the lower part which admit sufficient water to keep the level
within equal to the mean level without but which do not permit the admission of
water with sufficient rapidity to be affected by the waves. Within the box is a
copper float; in some cases this float carries a graduated vertical rod whose position
with reference to a fixed point of the box affords a measure for the height of the
water; in other gauges of this class the float is attached to a wire or cord which
passes over pulleys and terminates in a counterpoise whose position on a vertical
graduated scale shows the height of tide.
515. An Automatic Gauge requires a box and float such as has just been described.
The motion of the float in rising and falling with the tide is communicated to a pencil
which rests upon a moving sheet of paper; uniform motion is imparted to the paper
by the revolution of a cylinder driven by clockwork; the motion of the pencil clue to
the tide is in a direction perpendicular to the direction of motion of the paper, and
a curve is thus traced, of which one coordinate is time and the other height, The
paper, which is usually of sufficient length to contain a month s record, is paid out
from one cylinder, passes over a second whereon it receives the record and is rolled
upon a third cylinder, which thus contains the completed tidal sheet.
This gauge, besides giving a perfectly continuous record, has the further merit
of requiring but little of the observer s time. But its indications, both of tune and
heights, should be checked by occasional comparisons with the standard clock and
the staff gauge, the readings of which should be noted by hand at appropriate points
of the graphic record.
A newer type of automatic gauge prints the date, the time, and the stage of
the tide every five minutes on a paper tape.
CHAPTER XXI.
OCEAN CURRENTS.
516. An ocean current is a progressive horizontal motion of the water occurring
throughout a region of the ocean, as a result of which all bodies floating therein are
carried with the stream.
The set of a current is the direction toward which it flows, and its drift, the velocity
of the flow.
517. CAUSE. The principal cause of the superficial ocean currents is the wind.
Every breeze sets in motion, by its friction, the surface particles of the water over
which it blows; this motion of the upper stratum is imparted to the stratum next
beneath, and thus the general movement is communicated, eachlayer of particles acting
upon the one below it, until a current is established. The direction, depth, strength,
and permanence of such a current will depend upon the direction, steadiness, and force
of the wind; all, however, subject to modification on account of extraneous causes,
such as the intervention of land or shoals and the meeting of conflicting currents.
A minor cause in the generation of ocean currents is the difference in density of the
sea water in different regions, as a result of which a set is produced from the more
dense toward the less dense, in the effort to establish equilibrium of pressure; the
difference of density may be due to temperature, the warmer water near the equator
being less dense than the colder water of higher latitudes; or it may be created by a
difference in the amount of contained saline matter, resulting from evaporation,
freezing, or other causes. Another minor factor that may have influence upon ocean
currents is the difference of pressure exerted by the atmosphere upon the water in
different regions. But neither of the last-mentioned causes may be regarded as of
great importance when compared with the influence, direct and indirect, of the wind.
518. SUBMARINE CURRENTS. In any scientific investigation of the circulation
of ocean waters it is necessary to take account of the submarine currents as well
as those encountered upon the surface; but for the practical purposes of the navigator
the surface currents alone are of interest.
519. METHODS OF DETERMINATION. The methods of determining the exist
ence of a current, with its set and drift, may be divided into three classes; namely,
(a) by observations from a vessel occupying a stationary position not affected by the
current; (b) by comparison of the position of a vessel under way as given by obser
vation with that given by dead reckoning; and (c) by the drift of objects abandoned
to the current in one locality and reappearing in another.
520. Of these methods the first named, by observations from a vessel at anchor,
is by far the most accurate and reliable, but being possible only under special circum
stances is not often available. The most valuable information about ocean currents
being that which pertains to conditions in the open sea, the great depths there existing
usually preclude the possibility of anchoring a vessel; ships especially fitted for the
purpose have at times, however, carried out current observations with excellent
results; the most notable achievements in this direction are those of the survey of
the Gulf Stream, made by United States naval officers acting under the Coast and
Geodetic Survey, during which the vessel was anchored and observations were made
in positions where the depths reached to upward of 2,000 fathoms.
521. The method of determining current from a comparison of positions obtained
respectively by observation and by dead reckoning is the one upon which our knowl
edge must largely depend. This method is, however, always subject to some inac
curacy, and the results are frequently quite erroneous, for the so-called current is
thus made to embrace not only the real set and drift, but also the errors of observa
tion and dead reckoning. In the case of a modern steamer accurately steered and
equipped with good instruments for determining the speed through the water as well
as the position by astronomical observations, the current may be arrived at by this
method with a fairly close degree of accuracy. It is not always possible, however,
to keep an exact reckoning, and this is especially true in sailing vessels, where the
conditions render it difficult to determine correctly the position by account; this
232
OCEAN CURRENTS. 233
source of error ma^ be combined with faulty instrumental determinations, giving
apparent currents differing widely from those that really exist.
522. Much useful knowledge regarding ocean currents has been derived from
the observed drift of objects from one to another locality. This is true not only of
the bottles thrown overboard from vessels with the particular object of determining
the currents, but also of derelicts, drifting buoys, and pieces of wreckage, which
fulfill a similar mission. The deductions to be drawn from such drift are of a general
nature only. The point of departure, point of arrival, and elapsed time are all that are
positively known. The route followed and the set and drift of current at different points
are not indicated, and in the case of objects floating otherwise than in a completely
submerged condition account must be taken of the fact that the drift is influenced
by the wind. But even this general information is of great value in researches as to
ocean currents, and navigators who desire to aid in the work of investigation may do
so by throwing overboard, from time to time, sealed bottles containing a statement
of date and position at which they are launched.
523. CURRENTS OF THE ATLANTIC OCEAN. A consideration of the currents of
the Atlantic most conveniently begins with a description of the Equatorial Currents.
The effect of the northeast and southeast trade winds is to form two great drift cur
rents, setting in a westerly direction across the Atlantic from Africa toward the
American continent, whose combined width covers at times upward of fifty degrees
of latitude. These are distinguished as the Northern or Southern Equatorial Currents,
according as they rise from the trade ^inds of the northern or southern hemisphere.
Of the two, the Southern Equatorial Current is the more extensive. It has its
origin off the continent of Africa south of the Guinea coast, and begins its flow with
a daily velocity that averages about 15 miles; it maintains a general set of west, the
portion near the equator acquiring later, however, a northerly component, while the
drift steadily increases until, on arriving off the South American coast, a rate of 60
miles is not uncommon. At Cape San Roque the current bifurcates, the mam or
equatorial branch flowing along the Guiana coast, while the other branch is deflected
to the southward.
The Northern Equatorial Current originates to the northward of the Cape Verde
Islands and sets across the ocean in a direction that averages due west; though
parallel to the corresponding southern drift, its velocity is not so high.
524. Between the Northern and Southern Equatorial Currents is found the
Equatorial Counter Current setting to the eastward under the propelling force of the
southwest monsoon, which prevails over an elongated area of varying extent lying
north of the equator and "stretching westward from the southwestern part of the
salient extension of the continent of Africa. The extent and strength of this current
thus varies with the seasonal extent of the monsoon area, being a maximum in July
and August, when its effect is apparent to the westward of the fiftieth meridian of
west longitude, while at its minimum, in November and December, its influence is
but slight and prevails for only a limited distance from the African coast.
525. To the westward of the region of the Equatorial Counter Current the
North and the South Equatorial Currents unite. A large part of the combined
stream flows into the Caribbean Sea through the various passages between the
Windward Islands, takes up a course first to the westward and then to the northward
and westward, finally arriving off the extremity of the peninsula of Yucatan; from
here some of the water follows the shore line of the Gulf of Mexico, while another
portion passes directly toward the north Cuban coast; by the reuniting of these two
branches in the Straits of Florida there is formed the most remarkable of all ocean
currents the Gulf Stream.
From that portion of the combined equatorial currents which fails to find
entrance to the Caribbean Sea a current of moderate strength and volume takes its
course along the north coasts of Porto Rico, Haiti, and Cuba, flows between the
last-named island and the Bahamas, and enters the Gulf Stream off the Florida coast,
thus adding its waters to those of the main branch of the Equatorial Current which
have arrived at the same point bv wav of the Caribbean, the Yucatan Passage, and
the Gulf.
526. The Gulf Stream, which has its origin, as has been described, in the Straits
of Florida, and receives an accession from a branch of the Equatorial Current off
the Bahamas, flows in a direction that averages true north as far as the parallel x>f
234 OCEAN CURRENTS.
31, then curves sharply to ENE. until reaching the latitude of 32, when a direction
a little to the north of NE. is assumed and maintained as far as Cape Hatteras; at
this point its axis is about 40 miles, while its inner edge is in the neighborhood of 20
miles off the shore. Thus far in its flow the average position of the maximum current
is from 11 to 20 miles outside the 100-fathom curve, disregarding the irregularities
of the latter, and the width of the stream about 40 miles is nearly uniform. From
off Hatteras the stream broadens rapidly and curves more to the eastward, seeking
deeper water; its northern limit may be stated to be 60 to 80 miles off Nantucket
Shoals and 120 to 150 miles to the southward of Nova Scotia, in which latter place
it has expanded to a width of about 250 miles. Farther on its identity as the Gulf
Stream is lost, but its general direction is preserved in a current to be described later.
The water of the Gulf Stream is of a deep indigo-blue color, and its junction
with ordinary sea water may be plainly recognized; in moderate weather the edges
of the stream are marked by ripples ; in cool regions the evaporation from its surface,
due to difference of temperature between air and water, is apparent to the eye; the
stream carries with it a quantity of weed known as "gulf weed," which is familiar
to all who have navigated it waters.
In its progress from the tropics to higher latitudes the transit is so rapid that
time is not given for more than a partial cooling of the water, and it is therefore
found that the Gulf Stream is very much warmer than the neighboring waters of the
seas through which it flows. This warm water is, however, divided by bands of
markedly cooler water which extend in a direction parallel to the axis and are usually
found near the edges of the stream of warm water. The most abrupt change from
warm to cold water occurs on the inshore side, where the name of the Cold Wall has
been given to that band which has appeared to some oceanograDhers to form the
northern and western boundary of the stream.
The investigations of Pillsbury tend to prove that the thermometer is only an
approximate guide to the direction and velocity of the current. Though it indicates
the limits of the stream in a general way, it must not be assumed that the greatest
velocity of flow coincides with the highest temperature, nor that the northeasterly
set will be lost when the thermometer shows a region of cold sea water.
The same authority has also demonstrated that in the vicinity of the iand there
is a marked variation in the velocity of current at different hours of the day, which
may amount to upward of 2 knots, and which is due to the elevation and depression
of the sea as a result of tidal influences, the maximum current being encountered at
a period which averages about three hours after the moon s transit. Another effect
noted is that at those times when the moon is near the equator the current presents
a narrow front with very high velocity in the axis of maximum strength, while at
periods of great northerly or southerly decimation the front broadens, the current
decreasing at the axis and increasing at the edges. These tidal effects are not,
however, observed in the open sea.
The velocity of the Gulf Stream varies with the seasons, following the variation
in the intensity of the trade winds, to which it largely owes its origin. The drift of
the current under average conditions may be stated as follows :
Between Key West and Habana: Mean surface velocity in axis of maximum
current, 2\ knots; allowance to be made by a vessel crossing the entire width of the
stream, 1.1 knots per hour.
Off Fo wey Rocks : Mean surface velocity in axis, 3 .5 knots ; allowance in crossing,
2\ knots per hour.
Off Cape Hatteras: Mean surface velocity in axis, upward of 2 knots; allowance
in crossing the stream, 1J knots per hour between the 100-fathom curve and a point
40 miles outside that curve.
527. After passing beyond the longitude of the easternmost portions of North
America, it is generally regarded that the Gulf Stream, as such, ceases to exist; but
by reason of the prevalence of westerly winds the direction of the set toward Europe
is continued until the continental shores are approached, when the current divides,
one branch going to the northeastward and entering the Arctic regions and the other
running off toward the south and east in the direction of the African coast. These
currents have received, respectively, the designations of the Easterly, Northeast, and
Southeast Drift Currents.
. 528. The effect of the currents thus far described is to create a general circula
tion of the surface waters of the North Atlantic, in a direction coinciding with that
OCEAN CURRENTS. 235
of the hands of a watch, about the periphery of a huge ellipse, whose limits of latitude
may be considered as 20 N. and 40 N., and which is bounded in longitude by the
eastern and western continents. The central space thus inclosed, in which no well-
marked currents are observed, and in the waters of which great quantities of the
Sargasso or gulf weed are encountered, is known as the Sargasso Sea.
529. The Southeast Drift Current carries its waters to the northwest coast of
Africa, whence they follow the general trend of the land from Cape Spartel to Cape
Verde. From this point a large part of the current is deflected to the eastward close
along the upper Guinea coast. The stream thus formed, greatly augmented at certain
seasons by the prevailing monsoon and by the waters carried eastward with the
Equatorial Counter Current, is called the G-uima Current. A remarkable character
istic of this current is the fact that its southern limit is only slightly removed from
the northern edge of the west-moving Equatorial Current, the effect being that the
two currents flow side by side in close proximity, but in diametrically opposite
directions.
530. The Arctic or Labrador Current sets out of Davis Strait, flows southward
down the coasts of Labrador and Newfoundland, and thence southwestward past
Nova Scotia and the coast of the United States, being found inshore of the Gulf
Stream. It brings with it the ice so frequently met at certain seasons off New
foundland.
531. Eennells Current was formerly represented as a temporary but extensive
stream setting at tunes from the Bay of Biscay toward the west and northwest across
the English Channel and to the westward of Cape Clear. The most recent investiga
tions fail to reveal such a feature, but disclose only a narrow current of reaction
moving northward along the coast of France when the winds have forced the waters
above the usual level at the head of the Gulf of Gascoyne.
532. Of the two branches of the Southern Equatorial Current which are formed
by its bifurcation off Cape San Roque, the northern one, setting along the coasts of
northeastern Brazil and of Guiana and contributing to the formation of the Gulf
Stream, has already been described; the other, known as the Brazil Current, flows to
south and west, along the southeastern coast of Brazil, as far as the neighborhood
of the island of Trinidad; here it divides, one part continuing down the coast and
having some slight influence as far as the latitude of 45 S., and the other curving
around toward east.
533. The last-mentioned branch of the Brazil Current is called the Southern
Connecting Current and flows toward the African coast in about the latitude of Tristan
da Cunha. It then joins its waters with those of the general northerly current that
sets out of the Antarctic region, forming a current which flows to the northward along
the southwest African coast and eventually connects with the Southern Equatorial
Current, thus completing the surface circulation of the South Atlantic.
534. There is another current whose effects are felt in the Atlantic. It originates
in the Pacific and flows around Cape Horn, and will be described in connection with
the currents of the Pacific Ocean.
535. CURRENTS OF THE PACIFIC OCEAN. As in the Atlantic, the waters of the
Pacific Ocean, in the region between the tropics, have a general drift toward the
westward, due to the effect of the trade winds, the currents produced in the two
hemispheres being denominated, respectively, the Northern and the Southern Equa
torial Currents. These are separated, as also in the case of the Atlantic, by an east-
setting stream, about 300 miles wide, whose mean position is a few degrees north of
the equator, and which receives the name of the Equatorial Counter Current.
536. The major portion of the Northern Equatorial Current, after having
passed the Marianas, nows toward the eastern coast of Taiwan in a WNW. direc
tion, whence it- is deflected northward, forming a current which is sometimes
called the Japan Stream, but which more frequently receives its Japanese name of
Kuroshiwo, or "black stream." This current, the waters of which are dark in color
and contain a variety of seaweed similar to "gulf weed/ 7 carries the warm tropical
water at a rapid rate to the northward and eastward along the coasts of Asia^and its
offlying islands, presenting many analogies to the Gulf Stream of the Atlantic.
The limits and volume of the Kuroshiwo vary according to the monsoon, being
augmented during the season of southwesterly winds and diminished during the prev
alence of those from northeast. The current sets to the north along the east coast
of Taiwan (Formosa), and in about latitude 26 N. changes its course to northeast,
236 OCEAN CURRENTS.
arriving at the extreme southwestern point of Japan by a route to westward of the
Sakishima and Nansei Shoto. A branch makes off from the main stream to fol
low northward along the west coast of Japan, entering the Sea of Japan by the Tsu
shima Kaikyo; but the principal current bends toward the east, flows through
Osumi Kaikyo and the passages between the Tokara Gun to, and runs parallel to the
general trend of the south shores of the Japanese islands of Kiushu, Shikoku, and
Honshu, attaining its greatest velocity between Bungo Suido and Kii Suido, where
its average drift is between 2 and 3 knots per hour. Continuing beyond the south
eastern extremity of Honshu, the direction of the stream becomes somewhat more
northerly, and its width increases, with consequent loss of velocity. In the Kuro-
shiwo, as in the Gulf Stream, the temperature of the sea water is an approximate,
though not an exact, guide as to the existence of the current.
537. Near 146 or 147 E. and north of the fortieth parallel the Kuroshiwo
divides into two parts. One of these, called the Kamchatka Current, flows to the
northeast in the direction of the Aleutian Islands, and its influence is felt to a high
latitude. The second branch continues as the main stream, and maintains a general
easterly direction to the 180th meridian, where it is merged into the north and north
east drift currents which are generally encountered in this region.
538. A cold countercurrent to the Kamchatka Current sets out of Bering Sea
and flows to the south and west clpse to the shores of the Kuril Islands, Hokushu
and Honshu, sometimes, like the Labrador Current in the Atlantic, bringing with it
quantities of Arctic ice. This is often called by its Japanese name of Oyashiwo.
539. On the Pacific coast of North America, from about 50 N. to the mouth
of the Gulf of California, 23 N., a cold current, 200 or 300 miles wide, flows with a
mean speed of three-quarters of a knot, being generally stronger near the land than
at sea. It follows the trend of the land (nearly SSE.) as far as Point Concepcion
(south of Monterey), when it begins to bend toward SSW., and then to WSW., off
Capes San Bias and San Lucas, ultimately joining the great northern equatorial drift.
On the coast of Mexico, from Cape Corrientes (20 N.) to Cape Blanco (Gulf of
Nicoya), there are alternate currents extending over a space of more than 300 miles
in width, which appear to be produced by the prevailing winds. During the dry
season January, February, and March the currents generally set toward south
east; during the rainy season from May to October especially in July, August,
and September, the currents set to northwest, particularly from Cosas Island and
the Gulf of Nicoya to the parallel of 15.
540. The Southern Equatorial Current prevails between limits of latitude that
may be approximately given as 4 N. and 10 S., in a broad region extending from
the American continent almost to the one hundred and eightieth meridian, setting
always to the west and with slowly increasing velocity. In the neighborhood of the
Fiji Islands this current divides; one part, known as the Rossel Current, continues
to the westward, following a route marked by the various passages between the
islands, and later acquiring a northerly component and setting through Torres
Strait and along the north coast of New Guinea; the other part, called the Australia,
Current, sets toward south and west, arriving off the east coast of Australia, along
which it flows southward to about latitude 35 S., whence it bends toward southeast
and east and is soon after lost in the currents due to the prevailing wind.
541. The general drift current that sets to the north out of the Antarctic
regions is deflected until, upon gaining the regions to the southwest of Patagonia, it
has acquired a nearly easterly set; in striking the shores of the South American
continent it is divided into two branches.
The first, known as the Cape Horn Current, maintains the general easterly
direction, and its influence is felt, where not modified by winds and tidal currents,
throughout the vicinity of Cape Horn, and, in the Atlantic Ocean, off the Falkland
Islands and eastern Patagonia.
The second branch flows northeast in the direction of Valdivia and Valparaiso,
follows generally the direction of the coast lines of Chile and Peru (though at times
setting directly toward the shore in such manner as to constitute a great danger to
the navigator), and forms the important current which has been* called variously
the Peruvian, Chilean, or Ilumloldt Current, the last name having been given for the
distinguished scientist who first noted its existence. The principal characteristic of
OCEAN CURRENTS. 237
the Peruvian Current is its relatively low temperature. The direction of the waters
between Pisco and Payta is between north and northwest; near Cape Blanco the
current leaves the coast of America and bears toward the Galapagos Islands, passing
them on both the northern and southern sides; here it sets toward WXW. and west;
beyond the meridian of the Galapagos it widens rapidly, and the current is lost in
the equatorial current, near 108 W. As often happens in similar cases, the existence
of a countercurrent has been proved on different occasions; this sets toward the
south, is very irregular, and extends only a little distance from shore.
54:2. CURRENTS OF THE INDIAN OCEAX. In this ocean the currents to the
north of the equator are very irregular; the periodical winds, the alternating breezes,
and the changes of monsoon produce currents of a variable nature, their direction
depending upon that of the wind which produces them, upon the form of neighboring
coasts, or, at times, upon causes which can not be satisfactorily explained.
543. There is, in the Indian Ocean south of the equator, a regular Equatorial
Current which, by reason of owing its source to the southeast trade winds, corresponds
with the Southern Equatorial Currents of the Atlantic and Pacific. The limits of
this west-moving current vary with the longitude as well as with the season. Upon
reaching about the meridian of Rodriguez Island, a branch makes off toward the
south and west, flowing past Mauritius, then to the south of Madagascar (on the
meridian of which it is 480 miles broad), and thereafter, rapidly diminishing its
breadth, forming part of the Agulhas Current a little to the south of Port Natal.
The main equatorial current continues westward until passing the north end of
Madagascar, where, encountering the obstruction presented by the African con
tinent, it divides, one branch following the coast in a northerly, the other in a southerly
direction. The former, in the season of the southwest monsoon, is merged into the
general easterly and northeasterly drift that prevails throughout the ocean from the
northern limit of the Equatorial Current on the south, as far as India and the adjacent
Asiatic shores on the north; but during the northeast monsoon, when there exists in
the northern regions of the Indian Ocean a westerly drift current analogous to the
Northern Equatorial Currents produced in the Atlantic and Pacific by the northeast
trades, there is formed an e^st-setting Equatorial Counter current, which occupies a
narrow area near the equator and is made up of the waters accumulated at the
western continental boundary of the ocean by the drift currents of both hemispheres.
544:. The southern branch of the Equatorial Current flows to the south and west
down the Mozambique Channel, and, being joined in the neighborhood of Port Natal
by the stream which arrives from the open ocean, there is formed the warm Agulhas
Current, which possesses many of the characteristics of the Gulf and Japan streams.
This current skirts the east coast of South Africa and attains considerable velocity
over that part between Port Natal and Algoa Bay. During the summer months its
effects are felt farther to the westward; during the winter it diminishes in force and
extent. The meeting of the Agulhas Current with the cold water of higher latitudes
is frequently denoted by a broken and confused sea.
Upon arriving at the southern side of the Agulhas Bank the major part of the
current is deflected to the south, and then curves toward east, flowing back into the
Indian Ocean with diminished strength and temperature on about the fortieth
parallel of south latitude, where its influence is felt as far as the eightieth meridian.
A small part of the stream which reaches Agulhas Bank continues across the southern
edge of that bank before turning to the southward and eastward to rejoin the
major part.
545. Along the fortieth parallel of south latitude, between Africa and Australia,
there is a general easterly set, due to the branch of the Agulhas Current already
described, to the continuation of the drift current from the Atlantic which passes to
southward of the Cape of Good Hope, and to the westerly winds which largely prevail
in this region. At Cape Leeuwin, the southwestern extremity of Australia, this
east-setting current is divided into two branches; one, going north along the west
coast of Australia, blends with the Equatorial Current nearly in the latitude of the
Tropic of Capricorn; the other preserves the direction of the original current and
has the effect of producing an easterly set along the south coast of Australia.
54:6. As in the other oceans, a general northerly current is observed to set into
the Indian Ocean from the Antarctic regions.
CHAPTER XXII.
IOE AND ITS MOVEMENT IN THE NOETH ATLANTIC OCEAN.
547. Vessels crossing the Atlantic Ocean between Europe and the ports of the
United States and British America are liable to encounter icebergs or extensive
fields of compact ice, which are carried southward from the Arctic region by the
ocean currents. It is in the vicinity of the Great Bank of Newfoundland that these
APRIL
Limiting lines of the regions
in which icebergs and field ice
have been reported by mariners
in the month of April for the
years 1904 to 1913, inclusive.
masses of ice appear in the greatest numbers and drift farthest southward. The
accompanying charts show the changeable area in which icebergs and field ice have
been reported by mariners in the years 1904 to 1913 in the months of April, May,
and June, when they occur in the greatest number.
238
ICE AND ITS MOVEMENT IN THE NORTH ATLANTIC OCEAN. 239
. The amount of ice and its location and movement are so variable from year to
year, while the region occupied in its formation and transportation is so vast and
so little under special observation, that no successful system of prediction has as yet
been instituted. The most that can be said now is that after an exceptionally open
winter in the Arctic we may expect the ice to come south earlier and in greater quan
tity. After such a winter the East Greenland current starts the ice stream around
Cape Farewell from one to three months earlier, and this advancing of the season is
reflected by a corresponding advance in the Labrador Current and on the Newfound
land Bank. The greatest calving at the glaciers of Greenland follows the breaking
up of the shore ice, and hence the bergs also start southward earlier and with more
freedom after an open winter.
In April, May, and June, from 1904 to 1913, inclusive, icebergs have been seen
as far south as latitude 37 50 north and as far east as longitude 38 west. Excep
tional drifts have occurred almost down to latitude 30 north, and between longi
tudes 10 and 75 west, in these months as well as during other seasons of the year.
Between Newfoundland and the fortieth parallel floating ice may be met in any
month, but not often from August to December. On the Great Bank of New
foundland bergs generally move southward. Those that drift westward of Cape
Race usually pass between Green and St. Pierre banks. The Virgin Rocks are
generally surrounded by ice until the middle of April or the beginning of May.
548. THE ORIGIN OF THE ICEBERGS. -Most of the bergs which annually appear
in the North Atlantic originate on the western coast of Greenland; a few come from
the east coast and from Hudson Bay. A small but productive glacier in southern
Greenland yields the bluish bergs which are so hard to see at night. The largest
bergs come from the glaciers at Umaiiak Fjord and Disko Bay (Lat. 69 to 71), and
their height above water will rise to 500 feet; but as they lose in mass from that time
forward, we can not expect to find them of such gigantic height when they finally
appear near the Newfoundland Bank.
A huge ice sheet, formed from compressed snow, covers the whole of the interior of
Greenland. The surface of this enormous glacier, only occasionally interrupted by
protruding mountain tops, rises slightly toward the interior and forms a watershed
between the east and west coasts, which is estimated to be from 8,000 to 10,000 feet
above the sea. The outskirts of Greenland, as they are called, consist of a fringe
of islands, mountains, and promontories surrounding the vast ice-covered central
portion and varying in width from a mere border up to 80 miles. Upon the west
side, below the parallel of 73 of latitude, it has an average width of about 50 miles
and extends with little interruption from Cape Farewell to Melville Bay, a distance
of something over 1,000 miles.
Everywhere this mountainous belt is penetrated by deep fiords, which reach
to the inland ice, and are terminated by the perpendicular fronts of huge glaciers,
while in some places the ice comes down in broad projections close to the margin of
the sea. All of these glaciers are making their way toward the sea, and, as their
ends are forced out into the water, they are broken off and set adrift as bergs. This
process is called calving. The size of the pieces set adrift varies greatly, but a berg
irom 60 to 100 feet to the top of its walls, whose spires or pinnacles may reach from
200 to 250 feet in height and whose length may be from 300 to 500 yards, is considered
to be of ordinary size in the Arctic. These measurements apply to the part above
water, which is about one-eighth or one-ninth of the whole mass. Many authors-
give the depth under water as being from eight to nine times the height above; this
is incorrect, as measurements above and below water should be referred to mass and
not to height.
Bergs are being formed all the year round, but in greater numbers during the
summer season; and thousands are set adrift each year.
Once adrift in the Arctic they find their way into the Labrador Current and
begin their journey to the southward. It is not an unobstructed drift, but one
attended with many stoppages and mishaps. Many ground in the Arctic Basin and
break up there: others reach the shores of Labrador, where from one end to the
other they continually ground and float; some break up and disappear entirely,
while others get safely past and reach the Grand Bank. The whole coast of Labrador
is cut up by numerous islands, bays, and headlands, shoals and reefs, which makes the
240
ICE AND ITS MOVEMENT IN THE NORTH ATLANTIC OCEAN.
journey of all drift a long one, and adds greatly to the destruction of the bergs by stop-
Eages and by causing them to break up. Disintegration is also hastened by their
reaking away from the floe ice, for detached bergs will melt and break up rapidly
even in high latitudes during the summer.
549. THE ICE-BEARING CURRENTS. The Labrador Current passes to the
southward along the coasts of Baffin Land and Labrador, and, although it occasionally
ceases altogether, its usual rate is from 10 to 36 miles per day. Near the coast it is
very much influenced by the winds, and reaches its maximum rate after those from
MAY
Limiting lines of the regions
in which icebergs and field ice
have been reported by mariners
in the month of May for the
years 1904 to 1913. inclusive.
FIG. 79.
the northward. The general drift of the current is to the southward, as shown by
the passage of many icebergs, although occasions have arisen on which these have
been observed to travel northward without any apparent reason. The breadth and
depth of the current are not known, but it is certain that it pours into the Atlantic
enormous masses of water for which compensation is derived from the warm waters
of the Atlantic and from the East Greenland Current that flows around Cape Farewell.
The flow of the Polar Current down the east coast of Greenland has been abundantly
demonstrated by the drift of vessels that have been beset in the ice pack to the east
ward of Greenland. This current turns around Cape Farewell, with an ice stream
ICE AND ITS MOVEMENT IN THE NORTH ATLANTIC OCEAN. 241
60 miles wide, and then takes a northwesterly direction along the Greenland coast
as far as the Arctic Circle, where it meets the southerly current from Baffin Bay.
550. DRIFT AND CHARACTERISTICS OF ICEBERGS. Xot all the bergs made in
any one season find their way south during the following one, for only a small per
centage of them ever reach trans-Atlantic routes. So many delays attend tneir
journey and so irregular and erratic is it that many bergs seen in any one season
may have been made several seasons before. If bergs on their calving at once drifted
to the southward and met with no obstructions their journey of about 1,200 to 1,500
miles would occupy from 4 to 5 months, reckoning tne drift of the Labrador Current
at 10 miles a day, which may be making it too little. Then, if bergs were liberated
principally in July and August they should reach trans-Atlantic routes in December
and January, while we know this to be the rare exception. It is then seen what an
important bearing the shores of Labrador have in arresting their flow, when it is
known that bergs are generally most plentiful in the late spring and early summer
months off the Bank.
It should not be supposed that all bergs follow the same course when set adrift
from their parent glaciers, for, like floating bodies at the head of a river, some will
go direct to the mouth, others will go but a short distance and lodge, others still will
accomplish hah* the journey and remain until another freshet again floats them, so
that in the end the debris will be composed in part of that of several years production.
Bergs, when first liberated on the west Greenland shore, are out of the strongest
sweep of the southerly current, and they may take some months to find their way
out of Davis Strait, while again others may at once drift into the current and move
unobstructed until dissipated in the Gun Stream. The difference in time of two
bergs reaching a low latitude, which were set adrift the same day, may cover a period
of one or two years.
Field ice also offers an obstruction to bergs, and a close season in the Arctic
may prevent their liberation to a great extent, though, from their deep submersion,
they act as ice plows and aid materially in breaking up the vast fields of ice which
so often close the Arctic Basin.
Ice fields are more affected by wind than bergs. Bergs owe their drift almost
entirely to current, so that they will often be noticed forcing their way through
immense fields of heavy ice and going directly to windward. Advantage is taken of
this by vessels in ice fields, which often moor to bergs and are towed for miles through
ice in which they could not otherwise make any headway. This is accomplished by
sinking an ice anchor into them and using a strong towline, and as the berg advances
open water is left to leeward while the loose ice floats past on both sides. For the
same reason vessels, when beset by field ice, run from the lee of one berg to that of
another, as leads may offer themselves.
Instances are not rare where icebergs were seen to drift toward north, making
15 to 24 miles a day, near the tail of the Bank and to the eastward of Cape Race.
All ice is brittle, especially that in bergs, and it is wonderful how little it takes
to accomplish then" destruction. A blow of an ax will at times split them, and the
report of a gun, by concussion, will accomplish the same end. They are more apt
to break up in warm weather than cold, and whalers and sealers note this before
landing on them, when an anchor is to be planted or fresh water to be obtained. On
the coast of Labrador in July and August, when it is packed with bergs, the noise of
rupture is often deafening, and those experienced in ice give them a wide berth.
When they are frozen the temperature is very low, so that when their surface
is exposed to a thawing temperature the tension of the exterior and interior is very
different, making them not unlike a Prince Rupert s drop. Then, too, during the
day water made by melting finds its way into the crevices, freezes, and hence expands,
and, acting like a wedge, forces the berg into fragments. It is the greatly increased
surface which the fragments expose to the melting action of the oceanic waters that
accounts for the rapid disappearance of the ice after it has reached the northern
edge of the warm circulatory drift currents of the North Atlantic Ocean. If these
processes of disintegration did not go on and large bergs should remain intact, several
years might elapse before they would melt, and thev would ever be present in the
transoceanic routes. In fact, instances are on record in which masses of ice, escaping
the influences of swift destruction or possessing a capability for resisting them, have,
61828 16^ 16
242
ICE AND ITS MOVEMENT IN THE NORTH ATLANTIC OCEAN.
by phenomenal drifts, passed into European waters and been encountered from time
to time throughout that portion of the ocean which stretches from the British Isles
to the Azores.
Icebergs assume the greatest variety of shapes, from those approximating to
some regular geometric figure to others crowned with spires, domes, minarets, and
peaks, while others still are pierced by deep indentations or caves. Small cataracts
fall from the large bergs, while from many icicles hang in clusters from every pro-
JUNE
Limiting lines of the regions
in which icebergs and field ice
have been reported by mariners
in the month of June for the
years 1904 to 1913, inclusive.
FIG 80.
jecting ledge. They frequently have outlying spurs under water, which are as
dangerous as any other sunken reefs. For this reason it is advisable for vessels to
give them a wide berth, for there are cases on record where vessels were seriously
damaged by striking when apparently clear of the berg. Among these is that of the
British steamship Nessmore, which ran into a berg in latitude 41 50 N., longitude
52 W., and stove in her bows. On docking her a long score was found extending
from abreast her forerigging all of the way aft, just above her keel. Four frames were
ICE AND ITS MOVEMENT IN THE NOETH ATLANTIC OCEAN. 243
broken and the plates were almost cut through. The ship evidently struck a pro
jecting spur after her helm had been put over, as there was clear water between her
and the berg after the first collision.
It is generally best to go to windward of an iceberg, because the disintegrated
fragments will have a tendency to drift to leeward while open water will be found to
windward. Serious injury has occurred to vessels through the breaking up or cap
sizing of icebergs. Often the bergs are so nicely balanced that the slightest melting
of their surfaces causes a shifting of the center of gravity and a consequent turning
over of the mass into a new position, and this overturning also frequently takes
place when bergs, drifting with the current in a state of delicate equilibrium, touch
the ocean bottom.
551. FIELD ICE. Field ice is formed throughout the region from the Arctic
Ocean to the shores of Newfoundland and yearly leaves the shore to find its way
into the path of commerce. Starting with the Arctic field ice and conning to the
southward, we find this ice growing lighter, both in thickness and in quantity, until
it disappears entirely. Ice made in the Arctic is heavier and has lived through a
number of seasons. After the short summer in high latitudes ice begins to form on
all open water, increasing several feet in thickness each season. Much of this remains
north during the following summer, and, though it melts to some extent, it never
entirely disappears, so that each succeeding winter adds to its thickness.
This continues from year to year until it reaches 12 or 15 feet in thickness, often
more. If it remained perfectly quiet it would be of uniform thickness, increasing
with the latitude, but it is in a state of almost continual motion, often a very violent
one, which causes it to raft and pile until it becomes full of hummocks and other
irregularities. Immense fields are detached from the shore and from other fields,
and under the influence of winds, currents, and tides are set in motion and kept
continually drifting from place to place; after a snow, thaw, or piling the whole
becomes cemented together into solid pieces, when under the influence of a low
temperature. The space of open water between the fields becomes frozen, joining
smaller fields, and making a solid pack which will remain so until the elements again
break it to pieces. Along the shores from headland to headland the bays and inlets
often remain solid for years, almost invariably through the Arctic winter, but in
Baffin Bay and Davis Strait open water can be found at intervals all the year round.
Ice becomes rafted in a variety of ways. If two fields are adrift the one to
windward will drift down on the one to leeward; the one which is rougher on its
surface gives the wind a better hold and drifts the faster; fields may be impelled
towards each other by winds from contrary directions. Ice that is secure to the
shore is rafted on its seaward edge from contact with that which is adrift. Fields
in drifting often have a turning motion, which is caused by contrary currents, or one
variable in strength at different places, or by the friction of a field coming in contact
with another field afloat or one attached to the shore. This rotary motion is especially
dangerous when a vessel finds itself between two fields. A heavy gale will break up
the strongest fields at times and cause them to raft and form hummocks.
Small fragments of bergs find themselves mingled with Arctic fields and become
frozen fast. These, when liberated to the southward, are called growlers, and form
low, dark, indigo colored masses, which are just awash and rounded on top like a
whale s back. They are very dangerous when in ice fields which have become loose
enough to permit the passage of vessels through them, and should always be looked
for; they can be seen apparently rising and sinking as the sea breaks over them.
During the spring and summer months the bergs, aided by a rise of temperature,
so cut up and weaken the ice fields that much ice is loosened and begins drifting out
of the Arctic basin. This is joined by that brought from the waters of Spitsbergen by
the East Greenland Current, near the sixty-third parallel, whence it flows down the
eastern coast of North America, reaching Cape Chidley about October ^or November.
By this time the remaining ice in the Arctic is being cemented into solid fields, while
the ice cap is being daily extended to the southward. As fast as fields are detached
the open water freezes, and these masses are forced to the southward and can not
rejoin the solid pack. With a westerly wind ice formed in Hudson Strait and adjacent
waters is swept out and joins the Arctic ice, differing from it only in being a little
lighter.
244 ICE AND ITS MOVEMENT IN THE NORTH ATLANTIC OCEAN.
Ice begins to form at Cape Chidley about the middle of October, at Belle Isle
about November 1, and by the middle of November or 1st of December, the whole
coast is solidly frozen. The dates given are approximate and vary from year to
year, with many marked exceptions.
The string of ice along the coast of Labrador extends from headland to head
land, including the outlying islands, and starting from the heads of the bays works
its way out to seaward, forming by the middle of December an impassable barrier
to the shore which will probably not be permanently broken until the latter part of
April. This ice varies in thickness from 12 feet at the northern extreme to 3 or 4
feet at the southern. During the entire winter the Arctic drift is finding its way
down the coast, and is being continually reinforced by fields broken from the Labrador
ice. These continue to the southward in the Labrador Current on an average of
about 10 miles a day, reaching Belle Isle between the middle of January and the
middle of February.
The best example on record of a continued drift from the Arctic is that of Cap
tain Tyson. On October 14, 1871, he and a party of nineteen others were separated
from the United States surveying ship Polaris^ in latitude 77 or 78 N., just south of
Littleton Island, and, being unable to regain the ship, remained on the floe and
accomplished one of the most wonderful journeys. After a drift of over 1,500 miles,
fraught with danger from beginning to end, they were picked up about six months
later, April 30, 1872, by the Tigress, a sealing steamer from Newfoundland, near the
Strait of Belleisle, in latitude 53 35 N., and carried safely into port.
Much delay in the southward movement of the drift will be caused by winds
from the southward of west, as field ice is affected more by wind than current.
The prevailing wind and weather will influence the drift very greatly. Strong
northerly or northwest winds will increase its speed, but contrary winds will hold it
back. The string of shore ice keeps the northern ice off the coast and in the current,
At times westerly winds will also send the Labrador ice off the coast and leave it
entirely clear, but this does not happen often. Still the outer Labrador ice is con
stantly being added to the Arctic flow. Frequently the bays remain frozen over
until June; again, they are cleared some years in April, making a large variation.
During the drift the wind from northwest to southwest will clear the ice off the
coast and leave a line of open water, but the ice will be set on the coast by a northeast
wind and be rafted and piled. The appearance of the ice when it reaches Belle Isle
and to the southward would be a fair indication of the weather it had encountered
on its way down. The rougher the ice the more severe the weather. This floating
ice string extends approximately 200 miles offshore in the latitude of Cape Harrison,
and spreads more during its drift, though narrower farther north. One small stream
finds its way through the Strait of Belleisle, while the greater part continues toward
the northern limit of the Gulf Stream. By the middle of January the shores of
Newfoundland and Gulf of St. Lawrence are full of ice, which has been frozen there
and are opened or closed by a favorable or adverse wind. Navigation in the River
St. Lawrence is closed about the middle of November and does not open until about
May. A wind from northwest to southwest will clear the eastern coast of Newfound
land, while the Gulf of St. Lawrence may remain full of ice until the 1st of May.
Even after this date much ice is found in the Gulf until July, and by August or earlier
the field ice is replaced in the Strait of Belleisle by bergs.
In the bight from Cape Bauld to Fogo Island a string of ice is often found joining
these points, hemming in the shore for weeks at a time.
With each northwest or westerly wind the ice is cleared off the Newfoundland
coast, except from some of the deeper bays, and carried out to sea, and frequently
before the Arctic and Labrador ice has passed Belle Isle the Newfoundland ice has
found its way as far south as latitude 45. In the same way the Labrador ice some
times precedes the Arctic ice, while all may arrive at nearly the same time. Ice
fields of ten lose their identity , as coming from any one particular place, by the constant
intermingling on its southern journey with ice made in a lower latitude.
With easterly winds the field ice and icebergs may block the harbors on the
east coast of Newfoundland until June or even July, but these harbors are usually
open in May.
ICE AND ITS MOVEMENT IN THE NORTH ATLANTIC OCEAN. 245
Ice leaving the gulf and river St. Lawrence flows southward through Cabot Strait.
This strait is never frozen over completely, but vessels not specially built to encounter
ice can not navigate it safely between the beginning of January and the last of April on
account of the heavy drift ice which blocks the passage. Nearly every spring, from
about the middle of April to the middle of May, a great rush of ice out of the Gulf
of St. Lawrence causes a block between St. Paul Island and Cape Ray. This block,
which sometimes lasts for three or four weeks, and completely prevents the passage
of ships, is known as the bridge. It is recorded that 300 vessels have at one time been
detained by this obstacle.
The ice usually passes out of Cabot Strait in the direction of Banquereau Bank,
with its eastern edge extending halfway between Scatari and St. Pierre Islands.
Its path broadens after it is through the strait and is principally governed by the
winds, but, under the influence of the current alone, it drifts southwest-ward, and in
latitude 45 may be from 10 to 75 miles in width. Much of this ice is very heavy
and prevents the passage through it of all vessels that are not specially built to encoun
ter ice.
Ice fields assume a variety of shapes, depending upon the influence of winds
and currents, and upon their shape on being set adrift. Those loosened in the
Arctic meet with so many vicissitudes that they have entirely lost their original
form when a low latitude is reached, while those from Newfoundland may remain
approximately intact. Their extent is governed by the same rules and varies from
a few scattered pieces to several hundred miles in length.
From off Belle Isle the field ice finds its way south toward the Gulf Stream,
where no definite shape can be given it. In appearance, if heavy ice, it will be white,
covered with snow, and visible at a long distance; even in foggy weather it can often
be seen for some distance. It is full of hummocks and its surface is very uneven;
blocks have been piled upon each other, others stood on end, and the whole mass will
form an impenetrable field, through which vessels can not force their way.
If the ice is lighter the pans will be smoother and more even, the angles ground
down by friction and turned up at the edges like so many large pond lilies. If com
pact, no water is seen; if loose, wide leads may extend through the whole, or a little
water be seen surrounding each cake.
The appearance must decide whether a vessel is warranted in trying to force
her way through. In a smooth sea, where doubt exists, should a vessel go dead slow
into the mass, there will be but little danger in attempting it, and if too heavy she
can haul out. Often the weather edge is the heaviest from being rafted, when to
leeward it may be scattering. An ice field will often form a good lee for riding out a
gale of wind, as it will break the force of the sea. But care is necessary not to lie
too close, for the pans are often given such a force that they will stave in the bows
of the strongest vessel.
A high temperature will soften field ice and make it very rotten, so that the
slightest motion will cause it to fall to pieces. On reaching the waters of the Gulf
Stream or a warmer atmospheric temperature it begins to melt, gets soft and spongy,
and left in a calm will disappear slowly. But, fortunately, there is seldom a time
when there is not a swell on the sea, and this soon breaks the pans into small pieces,
thus bringing a greater surface in contact with the melting agency. A heavy gale
will in a few hours sometimes cause the destruction of a large field by fracture, friction,
and continued motion, just as a calm cold night may unite it in a solid mass. Bergs
plow their way through fields, break them up, and scatter the pieces, as in the Arctic.
Snow preserves them and often gives the pans the appearance of standing well out
of water, and is misleading in this particular. By melting and afterwarcLs freezing
it adds to the thickness of the ice.
552. THE DISAPPEARANCE OF THE ICE. The advancing ice will have reached,
in the month of April, the northern average limit of the Gulf Stream; and, having
spread itself along this line both east and west of the fiftieth meridian, it enters the
final stage of disintegration and rapid disappearance.
^ After reaching this limit of southward movement, many bergs, on account of
their deep immersion, find their way to the westward, even within the current of the
Gulf Stream, while field ice never follows this course, a condition that is accounted
246
ICE AND ITS MOVEMENT IN THE NORTH ATLANTIC OCEAN.
for by the fact that the Labrador current here runs under the Gulf Stream, which
spreads itself out on the surface as an eastward-moving current, consisting of streaks
of warm water with colder water between.
The locality in which ice of all kinds is most apt to be found during the months
of April, May, and June lies between latitude 42 and 45 and longitude 47 and 52
west of Greenwich. Here the Gulf Stream and the Labrador Current meet, and the
movement of the ice is influenced sometimes by the one and sometimes by the other
of these currents.
Stf
General enveloping lines of
the region of icebergs and field
ice, 1904-1913.
FlO. 81.
Besides the three charts of monthly limits for Amil, May, and June, a fourth
chart is presented showing the general limits within which icebergs and field ice hare
been encountered during the same months.
553. SIGNS OF THE PROXIMITY OF ICE. The proximity of ice is indicated by
the following-described signs :
Before field ice is seen from deck the ice blink will often indicate its presence.
On a clear day over an ice field on the horizon the sky will be much paler or lighter
in color and is easily distinguished from that overhead, so that a sharp lookout should
be kept and changes in the color of the sky noted.
ICE AND ITS MOVEMENT IN THE NORTH ATLANTIC OCEAN. 247
On a clear day icebergs can be seen at a long distance, owing to their brightness ;
during foggy weather they are first seen through the fog as a black object. In thick
fog the first sight of a berg is apt to be a narrow streak of dark at the water line.
They can sometimes be detected by the echo from the steam whistle or the
fog horn. In that case, by noting the time between the blast of a whistle and the
reflected sound, the distance of tne berg in feet may be approximately found by
multiplying by 550. The absence of echo is by no means proof that no bergs are
near, for unless there is a fairly vertical wall, no return of the sound waves can be
expected.
The presence of icebergs is often made known by the noise of their breaking up
and f ailing to pieces. The cracking of the ice or tne falling of pieces into the sea
makes a noise like breakers or a distant discharge of guns, which may often be heard
a short distance.
The absence of swell or wave motion in a fresh breeze is a sign that there is land
or ice on the weather side.
The appearance of herds of seal or flocks of murre far from land is an indication
of the proximity of ice.
The temperature of the air falls as ice is approached, especially on the leeward
side, but generally only at an inconsiderable distance from it. The fall of the tem
perature of the sea water has been held to indicate the nearness of ice, but in regions
where there is an intermixture of cold and warm currents going on, as at the junction
of the Labrador Current and the Gulf Stream, the temperature of the sea has been
known to rise as the ice is approached. The special temperature studies made during
the ice patrol of 1912 have not settled the question whether icebergs influence the
temperature of sea water to a measurable extent at distances of a mile or so.
A reliable sign of icebergs being near is the presence of calf ice. When such
pieces occur in a curved line, as they may do, especially in calm weather, the parent
berg is on the concave side of the curve.
No ship captain can afford to trust any of the above-named signs to the exclusion
of a good lookout.
CURRENT INFORMATION REGARDING ICE CONDITIONS. The branch hydrographic
offices receive daily the latest information regarding ice and other obstructions to
navigation, being furnished with the reports of passing vessels and the ice-patrol
ships, as long as such are in service. They also distribute the publications of the
Hydrographic Office dealing with this topic, namely, the Hydrographic Bulletin
(weekly) and the Pilot Chart (monthly), as well as the pamphlet on North Atlantic
Ice Patrols (Reprint No. 24).
APPENDIX I.
EXTBACTS FEOM THE AMERICAN NAUTICAL ALMANAC, FOE THE
YEAE 1916, WHICH HAVE EEFEEENCE TO THE EXAMPLES FOE
THAT TEAE GIVEN IN THIS WOEK.
G. M. T.
Sun s
Declination.
Equation
of Time.
Sun s
Declination.
Equation
of Time.
Sun s
Declination.
Equation
of Time.
Sun s
Declination.
Equation
of Time.
,
m s
m s
m s
,
m s
SUN, JANUARY, 1916.
Thursday 20.
Monday 24.
Friday 28.
-20 20. 8
-10 51. 7
-19 27.4
-11 58. 7
-18 28.2
-12 53. 5
2
20 19. 7
10 53. 2
19 26. 2
12 0.0
18 26. 9
12 54. 5
4
6
20 18. 7
20 17. 6
10 54. 7
10 56. 2
19 25.
19 23. 9
12 1.2
12 2.5
18 25. 6
18 24. 3
12 55. 5
12 56. 5
SEMIDIAMETER.
8
20 16. 5
10 57. 7
19 22. 7
12 3.7
18 23.
12 57. 4
10
20 15. 5
10 59. 2
19 21. 5
12 5.0
18 21. 7
12 58. 4
/
12
20 14. 4
11 0.7
19 20. 3
12 6.2
18 20. 4
12 59. 4
Jan. 1
16.30
14
20 13. 3
11 2.2
19 19. 1
12 7.4
18 19. 1
13 0.4
11
16.30
21
16.28
16
20 12. 3
11 3.7
19 17.9
12 8.7
18 17. 8
13 1.3
31
16.26
18
20 11. 2
11 5.2
19 16. 7
12 9.9
18 16. 5
13 2.3
20
20 10. 1
11 6.6
19 15. 5
12 11. 1
18 15. 1
13 3.3
22
-20 9. 1
-11 8. 1
-19 14. 3
-12 12.4
-18 13. 8
-13 4. 2
H. D.
0.5
0.7
0.6
0.6
0.7
0.5
SUN, APRIL, 1916.
Sunday 2.
Sunday 16.
Friday 21.
Tuesday 25.
+ 4 54. 5
- 3 41.
+10 6. 3
+ 9.4
+11 50. 5
+ 1 17. 2
+13 10.4
+2 3.3
2
4 56.4
3 39.5
10 8.1
10.6
11 52. 2
1 18.2
13 12.0
2 4.2
4
4 58.3
3 38.0
10 9.8
11.8
11 53. 9
1 19.3
13 13. 7
2 5.1
6
5 0.3
3 36.5
10 11. 6
13.0
11 55. 6
1 20.3
13 15. 3
2 6.0
8
5 2. 2
3 35.1
10 13. 4
14.2
11 57. 3
1 21.3
13 16.9
2 6.8
10
5 4.1
3 33.6
10 15. 1
15.4
11 59.
1 22.4
13 18. 6
2 7. 7
12
5 6.0
3 32.1
10 16. 9
16.6
12 0.7
1 23.4
13 20. 2
2 8. 6
14
5 7. 9
3 30.6
10 18. 7
17.8
12 2.4
1 24.4
13 21. 8
2 9.5
16
5 9.8
3 29.1
10 20. 4
19.0
12 4.1
1 25.4
13 23. 4
2 10.3
18
5 11.8
3 27.6
10 22. 2
20.2
12 5.8
1 26.4
13 25. 1
2 11.2
20
5 13.7
3 26.2
10 24.
21.4
12 7.4
1 27.4
13 26. 7
2 12.0
22
5 15. 6
3 24.7
+10 25. 7
+ 22. 6
12 9.1
1 28.4
13 28. 3
2 12.9
H. D.
1.0
0.7
0.9
0.6
0.8
0.5
0.8
0.4
Thursday 13.
Monday 17.
Saturday 22.
Wednesday 26.
+ 9 1.7
- 35. 6
+10 27. 5
+ 23. 8
+12 10. 8
+ 1 29. 4
+13 29. 9
+2 13. 7
2
9 3.5
34.3
10 29. 3
25.0
12 12. 5
1 30.4
13 31. 5
2 14.5
4
9 5.3
33.0
10 31.
26. 1
12 14. 2
1 31.4
13 33. 1
2 15.4
6
9 7. 2
31.7
10 32. 8
27. 3
12 15. 9
1 32.4
13 34. 7
2 16.2
8
9 9.0
30.5
10 34. 5
28.5
12 17. 5
1 33.4
13 36. 3
2 17.0
10
9 10.8
29.2
10 36. 3
29.6
12 19. 2
1 34.4
13 37. 9
2 17.9
12
9 12.6
27.9
10 38.
30.8
12 20. 9
1 35.4
13 39. 5
2 18.7
14
9 14.4
26.6
10 39. 8
32.0
12 22. 6
1 36.4
13 41. 1
2 19.5
16
9 16.2
25.4
10 41. 5
33.1
12 24. 2
1 37.3
13 42. 7
2 20.3
18
9 18.0
24.1
10 43. 3
34.3
12 25. 9
1 38.3
13 44. 3
2 21.1
20
9 19.8
22.8
10 45.
35.4
12 27. 6
1 39.3
13 45. 9
2 21.9
22
9 21.6
21.6
10 46. 8
36.6
12 29. 2
1 40.2
13 47. 5
2 22.7
H. D.
0.9
0.6
0.9
0.6
0.8
0.5
0.8
0.4
NOTE The Equation of Time is to be applied to the G. M. T. in accordance with the sign as given.
248
EXTRACTS FROM NAUTICAL, ALMANAC.
249
G. M. T.
Sun s
Declination.
Equation
of Time.
Sun s
Declination.
Equation
of Time.
Sun s
Declination.
Equation
of Time.
Sun s
Declination.
Equation
of Tune.
/
m s
m s
m s
,
m s
SUN, APRIL, 1916.
2
4
6
8
10
12
14
16
18
20
22
H. D.
Saturd
+ 9 44. 9
9 46.7
9 48.5
9 50.3
9 52.0
9 53.8
9 55.6
9 57.4
9 59.2
10 LO
10 2. 7
10 4.5
0.9
Ay 15.
+ 5. 2
4.0
2. 8
1.5
- 0.3
+ 0. 9
2.1
3. 3
4. 5
5. 8
7.0
8.2
0.6
Wednes
+11 9. 4
11 11. 1
11 12. 8
11 14. 6
11 16. 3
11 18.
11 19. 7
11 21. 4
11 23. 1
11 24. 9
11 26. 6
11 28. 3
0.9
dav 19.
-r "0 51. 3
52.4
53.5
54.6
55.7
56.8
57.9
59.0
1 0.1
1 1.2
122
1 3.3
0.5
Sunda
+12 30. 9
12 32. 6
12 34. 2
12 35. 9
12 37. 5
12 39. 2
12 40. 8
12 42. 5
12 44. 1
12 45. 8
12 47. 4
12 49. 1
0.8
y23.
-r 1 41. 2
1 42.2
1 43.1
1 44. 1
1 45.
1 46.0
1 46. 9
1 47.8
1 48.8
1 49.7
1 50.6
1 51.6
0.5
SEMIDIAMETER.
Apr. 1
11
21
May 1
16.03
15.98
15.94
15.90
SUN, MAY, 1916.
2
4
6
8
10
12
14
16
18
20
22
H. D.
Sunds
+18 37.
18 38. 2
18 39. 4
18 40. 6
18 41. 8
18 43.
18 44. 2
18 45. 4
18 46. 6
18 47. 8
18 49.
18 50. 2
0.6
ly 14.
+3 47. 5
3 47.5
3 47.5
3 47.5
3 47.5
3 47.5
3 47.5
3 47.5
3 47.5
3 47.5
3 47.5
3 47.5
0.0
Mond
+18 51. 4
18 52. 5
18 53. 7
18 54. 9
18 56. 1
18 57. 2
18 58. 4
18 59. 6
19 0.7
19 1.9
19 3.1
19 4.2
0.6
ay 15.
+3 47. 5
3 47.4
3 47.4
3 47.3
3 47.3
3 47.2
3 47.2
3 47.1
3 47.1
3 47.0
3 47.0
3 46.9
0.0
Wedr
+19 19. 1
19 20. 2
19 21. 3
19 22. 4
19 23. 6
19 24. 7
19 25. 8
19 26. 9
19 28.
19 29. 1
19 30. 3
19 31. 4
0.6
lesday 17.
+3 45. 7
3 45.6
3 45.5
3 45.3
3 45.2
3 45.0
3 44.9
3 44.8
3 44.6
3 44.5
3 44.3
3 44.2
0.1
Su
+20 10. 6
20 11. 6
nday 21.
+3 35. 6
3 35.2
SEMLDIAMETER.
May 1
11
21
31
15.90
15.86
15.83
15.80
SUN, JUNE, 1916.
2
4
6
8
10
12
14
16
18
20
22
H. D.
2
4
6
8
10
12
14
Wedne
+22 45. 2
22 45. 7
22 46. 2
22 46. 6
22 47. 1
22 47. 6
22 48.
22 48. 5
22 49.
22 49. 4
22 49. 9
22 50. 4
0.2
Mond
+23 26.
23 26. 1
23 26. 1
23 26. 2
23 26. 3
23 26. 3
23 26. 4
23 26. 4
sday 7.
+1 23. 2
1 22.3
1 21.3
1 20.4
1 19.4
1 18.5
1 17.6
1 16.6
1 15.7
1 14.7
1. 13 8
1 12.9
0.5
ay 19.
-1 3.6
1 4. 7
1 5.8
1 6. 9
1 8.0
1 9.0
1 10.1
1 11.2
Tuesd
+23 13.
23 13. 2
23 13. 5
23 13. 8
23 14.
23 14. 3
23 14. 6
23 14. 8
23 15. 1
23 15. 4
23 15. 6
23 15. 9
0. 1
Frids
+23 26. 5
23 26. 4
23 26. 3
23 26. 2
23 26. 2
23 26. 1
23 26.
23 25. 9
ay 13.
+0 12. 5
11.5
10.5
9.4
8. 4
7. 4
6.4
5. 3
4.3
3. 3
2.2
1.2
0.5
ly 23.
1 55. 5
1 56.6
1 57.6
1 58.7
1 59.8
2 0.8
2 1.9
2 3.0
Wednes
+23 27. 1
23 27. 1
23 27. 1
23 27. 1
23 27. 1
23 27. 1
23 27. 1
23 27. 1
23 27. 1
23 27. 1
23. 27
23 27.
0.0
Tuesd
+23 20. 3
23 20. 1
23 19. 9
23 19. 7
23 19. 4
23 19. 2
23 19.
23 18. 8
sday 21.
-1 29. 6
1 30.6
1 31.7
1 32.8
1 33.9
1 35.0
1 36.0
1 37.1
1 38.2
1 39.3
1 40.4
1. 41. 4
0.5
ay 27.
-2 46. 6
2 47.6
2 48.6
2 49.7
2 50.7
2 51.8
2 52.8
2 53.8
Sum
+23 24. 2
23 24. 1
23 23. 9
23 23. 8
23 23. 6
23 23. 5
23 23. 3
23 23. 2
23 23.
23 22. 9
23 22. 8
23 22. 6
0.1
lay 25.
-2 21. 2
2 22.3
2 23.4
2 24.4
2 25.5
2 26.5
2 27.6
2 28.6
2 29.7
2 30.8
2 31.8
2 32.9
0.5
SEMIDIAMETER.
June 1
11
21
July 1
15.80
15.78
15.77
15.76
NOTE. The Equation of Time is to be applied to the G. M. T. in accordance with the sign as given.
250
EXTEACTS FKOM NAUTICAL ALMANAC.
G. M. T.
Sun s
Declination.
Equation
of Time.
Sun s
Declination.
Equation
of Time.
Sun s
Decimation.
Equation
of Time.
Sun s
Declination.
Equation
ofTime.
h
,
m s
o ;
m s
,
m s
,
m s
SUN, JULY, 1916.
2
4
6
8
10
12
14
16
18
20
22
H. D.
Wedne
+21 59. 6
21 58. 9
21 58. 2
21 57. 5
21 56. 8
21 56. 1
21 55. 4
21 54. 7
21 54.
21 53. 3
21 52. 6
+21 51. 9
0.4
3day 12.
-5 23. 5
5 24.1
5 24.7
5 25.3
5 25.9
5 26.5
5 27.1
5 27.8
5 28.4
5 29.0
5 29.6
-5 30. 2
0.3
Monda
+19 53. 9
19 52. 8
19 51. 7
19 50. 7
19 49. 6
19 48. 6
19 47. 5
19 46. 4
19 45. 4
19 44. 3
19 43. 2
+19 42. 2
0.5
y24.
-6 18. 1
6 18.2
6 18.3
6 18.4
6 18.5
6 18.5
6 18.6
6 18.7
6 18.8
6 18.9
6 19.0
-6 19. 1
0.0
Friday
+19 0. 9
18 59. 8
18 58. 6
18 57. 4
18 56. 3
18 55. 1
18 53. 9
18 52. 8
18 51. 6
18 50. 4
18 49. 2
+18 48. 1
0.6
28.
-6 18. 8
6 18.7
6 18.6
6 18.5
6 18.4
6 18.3
6 18.2
6 18.1
6 18.0
6 17.9
6 17.8
-6 17. 6
0.1
SEMIDIAMETER.
July 1
11
21
31
/
15.76
15.76
15.77
15.79
SUN, OCTOBER, 1916.
2
4
6
8
10
12
14
16
18
20
22
H. D.
Sund
-3 9.8
3 11.7
3 13.7
3 15.6
3 17.5
3 19.5
3 21.4
3 23.4
3 25.3
3 27.2
3 29.2
3 31.1
1.0
ay 1.
+10 16. 1
10 17. 7
10 19. 3
10 20. 9
10 22. 5
10 24.
10 25. 6
10 27. 2
10 28. 8
10 30. 4
10 32.
10 33. 5
0.8
Thurs
-4 42. 7
4 44.6
4 46.5
4 48.4
4 50.4
4 52.3
4 54.2
4 56.1
4 58.1
5 0.0
5 1.9
5 3.8
1.0
day 5.
+11 30.4
11 31. 9
11 33. 4
11 34. 9
11 36.4
11 37. 9
11 39. 3
11 40. 8
11 42. 3
11 43. 8
11 45. 2
11 46. 7
0.7
Mond
-6 14.6
6 16.5
6 18.4
6 20.3
6 22.2
6 24.1
6 26.0
6 27.9
6 29.8
6 31.7
6 33.6
6 35.5
0.9
ay 9.
+12 39. 1
12 40. 5
12 41. 9
12 43. 2
12 44.6
12 45. 9
12 47. 3
12 48. 6
12 49. 9
12 51. 3
12 52. 6
12 53. 9
0.7
Friday 13.
-7 45. 2 +13 40. 8
SEMIDIAMETER.
Oct. 1
11
21
31
/
16.01
16.06
16.10
16.15
NOTE. The Equation of Time is to be applied to the G. M. T. in accordance with the sign as given.
EXTRACTS FROM NAUTICAL ALMANAC.
SUN, 1916.
251
Dy
Right Ascension of the Mean Sun at Greenwich Mean Noon. ,
Month.
January.
February.
March.
April.
May.
June.
h
m s
h
m s
h
m s
h m s
h m s
h m s
1
18
39 16. 2
20
41 29. 5
22 35 49. 6
38 2. 7
2 36 19. 4
4 38 32. 6
2
18
43 12.
;
20
45 26.
22 39 46. 1
41 59. 3
2 40 15. 9
4 42 29. 2
3
18
47 9.3
20
49 22. 6
22 43 42. 7
45 55. 8
2 44 12. 5
4 46 25. 7
4
18
51 5.9
20
53 19. 2
22 47 39. 2
49 52. 4
2 48 9.
4 50 22. 3
5
18
55 2.4
20
57 15.7
22 51 35. 8
53 49.
2 52 5. 6
4 54 18. 8
6
18
58 59.
21
1 12.3
22 55 32. 3
57 45. 5
2 56 2. 1
4 58 15. 4
7
19
2 55.5
21
5 8.8
22 59 28. 9
1
1 42.0
2 59 58. 7
5 2 12.0
8
19
6 52.1
21
9 5.4
23
3 25.4
1
5 38.6
3 3 55. 2
5 (
5 8.5
9
19
10 48. 7
21
13 1.9
23
7 22.0
1
9 35.2
3 7 51. 8
5 10 5. 1
10
19
14 45. 2
21
16 58. 5
23 11 18.6
1 13 31. 7
3 11 48. 4
5 14 1. 6
11
19
18 41. 8
21
20 55.
23 15 15. 1
1 17 28. 3
3 15 44. 9
5 17 58. 2
12
19
22 38. 3
21
24 51. 6
23
19 11.7
1 21 24. 8
3 19 41. 5
5 21 54. 8
13
19
26 34.9
21
28 48. 2
23 23 8. 2
1 25 21.4
3 23 38.
5 25 51. 3
14
19
30 31. 4
21
32 44. 7
23 27 4. 8
1 29 17. 9
3 27 34. 6
5 29 47. 9
15
19
34 28.0
21
36 41. 3
23 31 1. 3
1 33 14. 5
3 31 31. 2
5 33 44. 4
16
19
38 24. 6
21
40 37. 8
23 34 57. 9
1 37 11.
3 35 27. 7
5 37 41.
17
19
42 21. 1
21
44 34.4
23 38 54. 4
1 41 7. 6
3 39 24. 3
5 41 37. 6
18
19
46 17.7
21
48 30. 9
23 42 51.
1 45 4. 2
3 43 20. 8
5 45 34. 1
19
19
50 14. 2
21
52 27. 5
23 46 47. 5
1 49 0. 7
3 47 17. 4
5 49 30. 7
20
19
54 10.8
21
56 24.
23 50 44. 1
1 52 57. 3
3 51 13. 9
5 53 27. 2
21
19
58 7.4
22
20.6
23 54 40. 6
1 56 53. 8
3 55 10. 5
5 57 23. 8
22
20
2 3.9
22
4 17.1
23 58 37. 2
2
50.4
3 59 7.0
6 1 20.3
23
20
6 0.5
22
8 13.7
2 33.8
2
4 46.9
4 3 3. 6
6 5 16. 9
24
20
9 57.0
22
12 10. 2
6 30.3
2
8 43.5
4 7 0.2
6 9 13.5
25
20
13 53. 6
22
16 6.8
10 26. 9
2 12 40.
4 10 56. 7
6 13 10.
26
20
17 50.1
22
20 3.4
14 23. 4
2 16 36. 6
4 14 53. 3
6 17 6. 6
27
20
21 46. 7
22
23 59. 9
18 20.
2 20 33. 1
4 18 49. 8
6 21 3. 1
28
20
25 43. 2
22
27 56. 5
22 16. 5
2 24 29. 7
4 22 46. 4
6 24 59. 7
29
20
29 39. 8
22
31 53.
26 13. 1
2 28 26. 2
4 26 43.
6 28 56. 2
30
20
33 36.4
22
35 49. 6
30 9. 6
2 32 22. 8
4 30 39. 5
6 32 52. 8
31
20
37 32.9
22
39 46. 1
34 6.2
2 36 19.4
4 34 36. 1
6 36 49. 4
CORRECTION TO BE ADDED TO R. A. M. S. AT G.
M. N. FOR TIME PAST NOON.
Time.
QIC
6-
12 m
18 m
24 m
30*
36
49m
48 m
54 m
GO*
Time.
h
m s
m s
m s
m s
m s
m s
m s
m s
m s
m s
m s
h
0.0
1.0
2.
3.0
3. 9
4.9
5. 9
6.9
7.9
8.9
9.9
1
9.9
010.8
011.8
12.8
013.8
014.8
015.8
016.8
017.7
018.7
019.7
1
2
019.7
020.7
021.7
022.7
023.7
024.6
025.6
026.6
027.6
028.6
029.6
2
3
029.6
030.6
031.5
032.5
033.5
034.5
035.5
036.5
037.5
038.4
039.4
3
4
039.4
040.4
041.4
042.4
043.4
044.4
045.3
046.3
047.3
048.3
049.3
4
5
049.3
050.3
051.3
052.2
053.2
054.2
055.2
056.2
057.2
058.2
059.1
5
6
059.1
1 0. 1
1 1. 1
1 2.1
1 3. 1
1 4.1
1 5.1
1 6.0
1 7.0
1 8.0
1 9.0
6
7
1 9.0
1 10.0
1 11.0
1 12.0
1 12.9
113.9
1 14.9
1 15.9
116.9
117.9
118.9
7
8
118.9
119.8
120.8
121.8
122.8
123.8
124.8
125.7
126.7
127.7
128.7
8
9
128.7
129.7
130.7
131.7
132.7
133.6
134.6
135.6
136.6
137.6
138.6
9
10
138.6
139.6
140.5
141.5
142.5
143.5
144.5
145.5
146.5
147.4
148.4
10
11
148.4
149.4
150.4
151.4
152.4
153.3
154.3
155.3
156.3
157.3
158.3
11
252
EXTRACTS FEOM NAUTICAL ALMANAC.
SUN, 1916.
Day
Right Ascension of the Mean Sun at Greenwich Mean Noon.
of
Month
July.
August.
September.
October.
November.
December.
h
na s
h
m s
h
m s
h
m s
h m s
h m s
1
6
36 49. 4
8
39 2.6
10
41 15.8
12 39 32. 4
14 41 45. 6
16 40 2. 3
2
6
40 45. 9
8
42 59. 2
10
45 12. 4
12 43 29.
14 45 42. 2
16 43 58. 9
*
6
44 42. 5
8
46 55. 8
10
49 9.0
12 47 25. 6
14 49 38. 7
16 47 55. 4
4
6
48 39.
8
50 52. 3
10
53 5.5
12 51 22. 1
14 53 35. 3
16 51 52.
5
6
52 35. (
1
8
54 48.9
10
57 2.1
12 55 18. 7
14 57 31. 8
16 55 48. 6
I
5
6
56 32. 2
8
58 45. 4
11
58.6
12 59 15. 2
15 1 28.4
16 59 45. 1
7
7
28.7
9
2 42.0
11
4 55.2
13
3 11.8
15 5 25.
17
3 41.7
8
7
4 25.3
9
6 38.5
11
8 51.7
13
7 8.3
15 9 21. 5
17
7 38.2
3
7
8 21.
>
9
10 35. 1
11
12 48. 3
13 11 4. 9
15 13 18. 1
17 11 34. 8
10
7
12 18.4
9
14 31. 6
11
16 44. 8
13 15 1. 4
15 17 14. 6
17 15 31.4
11
7
16 14. 9
9
18 28. 2
11
20 41. 4
13 18 58.
15 21 11. 2
17 19 27. 9
12
7
20 11. 5
9
22 24. 8
11
24 37. 9
13 22 54. 5
15 25 7. 7
17 23 24. 5
13
7
24 8.1
9
26 21. 3
11
28 34. 5
13 26 51. 1
15 29 4. 3
17 27 21.
14
7
28 4.6
9
30 17. 9
11
32 31.
13 30 47. 6
15 33 0. 8
17 31 17. 6
15
7
32 1.2
9
34 14.4
11
36 27. 6
13 34 44. 2
15 36 57. 4
17 3
5 14.1
16
7
35 57. 7
9
38 11.
11
40 24. 2
13 38 40. 8
15 40 54.
17 39 10. 7
17
7
39 54. 3
9
42 7.5
11
44 20. 7
13 42 37. 3
15 44 50. 5
17 43 7. 3
18
7
43 50. 8
9
46 4.1
11
48 17. 3
13 46 33. 9
15 48 47. 1
17 47 3. 8
19
7
47 47. 4
9
50 0.6
11
52 13. 8
13 50 30. 4
15 52 43. 6
17 51 0. 4
20
7
51 44.
9
53 57. 2
11
56 10.4
13 54 27.
15 56 40. 2
17 54 56. 9
21
7
55 40. 5
9
57 53. 8
12
6. 9
13 58 23. 5
16 36. 8
17 58 53. 5
22
7
59 37. 1
10
1 50.3
12
4 3.5
14
2 20.1
16 4 33. 3
18
2 50.0
23
8
3 33.6
10
5 46.9
12
8 0.0
14
6 16.6
16 8 29. 9
18
6 46.6
24
8
7 30.2
10
9 43.4
12
11 56. 6
14 10 13.2
16 12 26.4
18 10 43. 2
25
8
11 26. g
10
13 40.
12
15 53. 1
14 14 9. 7
16 16 23.
18 14 39. 7
26
8
15 23. 3
10
17 36. 5
12
19 49. 7
14 18 6. 3
16 20 19. 5
18 18 36. 3
27
8
19 19. 9
10
21 33. 1
12
23 46. 2
14 22 2. 8
16 24 16. 1
18 22 32. 8
28
8
23 16.4
10
25 29. 6
12
27 42. 8
14 25 59. 4
16 28 12. 6
18 26 29. 4
29
8
27 13.
10
29 26. 2
12
31 39. 3
14 29 56.
16 32 9. 2
18 30 26.
30
8
31 9.5
10
33 22. 7
12
35 35. 9
14 33 52. 5
16 36 5. 8
18 34 22. 5
31
8
35 6.1
10
37 19. 3
12
39 32. 4
14 37 49. 1
16 40 2. 3
18 38 19. 1
CORRECTION TO
BE ADDED TO R. A. M. S
AT G
M. N.
FOR TIME PAST NOON.
Time.
0m
6 m
12 m
18 m
24 m
30 m
36 m
42 m
48 m
54 m
60 m
Time.
h
m s
m s
m s
m s
m s
m s
m s
m s
m s
m s
m s
h
12
158.3
159.3
2 0.2
2 1.2
2 2. 2
2 3. 2
2 4. 2
2 5. 2
2 6. 2
2 7.1
2 8.1
12
13
2 8.1
2 9.1
210.1
211.1
212.1
213.1
2 14.0
215.0
2 16.0
2 17.0
218.0
13
14
218.0
219.0
220.0
220.9
221.9
222.9
223.9
224.9
225.9
226.9
227.8
14
15
227.8
228.8
229.8
230.8
2 31. 8
232.8
233.8
234.7
235.7
236.7
237.7
15
16
237.7
238.7
239.7
240.7
241.6
242.6
243.6
244.6
245.6
246.6
247.6
16
17
247.6
248.5
249.5
2 50.5
251.5
252.5
253.5
254.5
255.4
256.4
257.4
17
18
257.4
258.4
259.4
3 0.4
3 1\4
3 2.3
3 3.3
3 4. 3
3 5. 3
3 6. 3
3 7.3
18
19
3 7. 3
3 8. 3
3 9.2
310.2
311.2
312.2
313.2
314.2
315.2
316.1
317.1
19
20
317.1
318.1
319.1
320.1
321.1
322.1
323.0
324.0
325.0
326.0
327.0
20
21
327.0
328.0
329.0
329.9
330.9
331.9
332.9
333.9
334.9
335.9
336.8
21
22
336.8
337.8
338.8
339.8
340.8
341.8
342.8
343.7
344. 7
345.7
346.7
22
23
346.7
347.7
348.7
349.7
350.6
351.6
352.6
353.6
354.6
3 55. 6
356.6
23
EXTRACTS FROM NAUTICAL ALMANAC.
MOON, 1916.
253
G. M. T.
Right
Ascension.
Declination.
S. D.
H. P.
G. M. T.
Right
Ascension.
Declination.
S. D.
H. P.
April
15.
May 6.
h
h m s
/
h
h
m s
!
11 20 23 ,,
+ 19. 2 _
15.5
56.9
6 15 36
+25 48. 6 .
14. 8 j 54. 2
2
11 24 18 S.
10. 2 ~
15.6
57.0
2
6 19 58 ^
25 42. 2 ^
14. 8 54. 2
4
11 28 14 f?
39. 8 S
15.6
57.1
4
6 24 19 *}
25 35. 2
14.8
54.2
6
113210^
]
15. C
57.1
6
62840JJ
25 27. 8 78
14. 8 54. 2
8
11 36 7 oq
]
. 38. 9 _
15.6
57.2
8
6 33
25 20. _
14.8
54.2
10
12
11 40 5 5?
11 44 3 !r!
C R zy/
2 8. 6
2 38. 3 5!
15.6
15.6
57.3
57.3
10
12
6 37 19
6 41 38 2
25 11. 6 I
25 2.8 ~
14.8
14.8
54.1
54.1
14
1148 2
3 8.0^
15.7
57.4
14
64556^
2453.5 f 7
14.8
54.1
16
11 52 2 0<
3 37. 7
15.7
57.5
16
6 50 13
24 43.8..
14.8
54.1
18
11 56 3 S
, ,_ K 298
4: /. O -_
15.7
57.5
18
65430^? 2433.6^
14.8
54.1
20
12 5r!f
4 37. 2 ^
15.7
57.6
20
6 58 45 5! 24 22. 9 ZT!
14.8
54.1
22
12
4 7
243
5 6 9 296
15.7
57.6
22
7
3 o r; 24 11. s :;t
zo- no
14.8
54.1
July
10.
October 10.
14 35 34 9a _ -20 37.9 _
16.0
58.7
16 45 , + 6 59. 3 _
16.0 f 58.6
2
14 40 19 f
20 57. 8 _
16.0
58.8
2
21 f??
7.28,73
16.0
58.5
4
14 45 6 tr
17. 2
16.1
58.9
4
25 15 S
7 58.
16.0
58.5
6
14 49 55 5?
o
36. 2 10
16.]
58.9
6
29 30 .
i
3 27. 1 =
16.0
58.5
zyi
186
^00
2SS
8
14 54 46 ,
21 54.8 1Q
16.1
59.0
8
33 45
8 55. 9
15.9
58.4
10
14 59 39 ;:
22 12 8
16.]
59.1
10
38 1 2
9 24. 5 f:
15.9
58.4
12
15 4 35 f:
22 30. 4 JS
16.1
59.2
12
o 42 16 rr
9 52. 9 ^
15.9
58.3
14
15 9 32
2*47.4
16.2
59.2
14
04633^
10210^
15.9
58.3
16
15 14 31
23 3.9 1(;
16.2
59.3
16
50 49 ^
10 48. 9 _
15.9
58.2
18
15 19 33 *
23 19. 8 U
16.2
59.4
18
55 6 ._
11 16. 5 ?
15.9
58.2
20
15 24 36 JJ
23 35. 2 J2
16.2
59.5
20
59 23 Zl
11 43. 8
15.9
58.1
22
15 29 41 J?
23 50. ! .
16.2
59.5
22
1
3 4irr
12 10. 8 f ?
15.9
58.1
24
15 34 48 J
-24 4. 2 " z 16. 3 59. 6
24
1
7 59 *>* 4-12 37. 6 ^
15.8
58.0
TIME OF TRANSIT, MERIDIAN OF GREENWICH.
h m
h
m
h m
h m
Feb. 16
10 37
May 20
15
29
June 18
15 12 .,
July 10
7 40 An
17
11 23 4f
21
16
28
19
16 5 r:
11
8 40 b(
Apr. 14
9 21 44
22
17
21 S
20
16 53 *
18
15 33 ._
15
10 5 ^
23
18
10 4
21
17 40 4
19
16 20 *
JUPITER, 1916.
GREENWICH MEAN TIME.
Date.
Ascension.
Apparent
Declination.
Transit,
Meridian
of Green
wich.
Date.
Apparent
Right
Ascension.
Apparent
Declination.
Transit,
Meridian
of Green
wich.
Noon.
Abo*.
Noon.
Noon.
h m s
o /
h m
h m s
1
h m
Apr. 15
16
56 28 _.
57 22
+ 4 51. 5
4 57. J!
23 20
23 17
Sept. 15
16
2 11 38 t .
2 11 22 "
+11 41. 1
11 39. 5
16
14 33
14 28
July 25
2 8 20 ,
+11 35. 9 ?!
17 54
17
2 11 5 J
f
m .
11 37. 9
16
17
14 24
26
9 C 49 ^
** 22
+1137.6 ;
17 51
18
2 10 48
i
s
11 36. 2
I/
17
14 20
Polar Semidiameter: July 1, .30; Aug. 1, .33;
Hor. Parallax: Apr. 1, .26; May 1, .27; July 1
Sept. 1, .36; Oct. 1, .39; Nov. 1, .39; Dec. 1, .37; Dec. 32, .34.
O .OS; Aug. 1, O .OS; Sept. 1,0 .03; Oct. 1,,0 .04; Nov. 1, .04; Dec. 1, .04;
Dec. 32, (X.03.
VENUS, 1916.
GREENWICH MEAN TIME.
Apr 16
438 4 267
+2514.7 no
3 1
June 1
7 17 48 w
+24 48. 5
93
2 39
Semidameter: Jan. 1, .IO; Feb. 1, .ll; Mar. 1, OM3; Apr. 1, OM6; May 1,
.22; Junel,0 .34;
Julvl,0 .49
Hor. Parallax: Jan. 1, .IO; Feb. 1, .ll; Mar. 1, .13; Apr. 1, .16; May 1
,0 .22; June 1,0
35
July 1,0 . 50.
253a
EXTKACTS FEOM NAUTICAL, ALMANAC.
OtOCOCNlO CN CO OS
CO 3 CN -Ji ?O CO ^ (TO CO CN ip rH rH rH
I -2ny
00 CO -if O *< CN CN G5 OS t~
CO ^F CN "?* iO CO CO CO CN
Ot^- COOOCNtOt- CN CD CO t^"cb i-HCO OOCN
CO to rH cd CO ^lOCNt^CN CN CN CO OS" TJ*
CO t^ CO CO O
OO CO CO rH t * r OS CO ft CO TPt^tOOOCO CN^COrHCO
O rH CO CO T)5 to CN t^ CN CN CN CO O5 *
OtOCStrH rH (NrHCN rH COCOrH
03 co t-- oso
Tl^ rH CO f>^ t
CN CN Tf >O CO
co oco t>.o>o
rH S CM 5? fo CO
^ ^co tocp
IO rH rH rH CN
~co"w oo" 06 1- r- rH to o co
OI>OS"3 COcOtOOCN
cOCSl^CN CN(NO(5C5-^
OS OC 1 1^- CO O>
~CO~l>~f-^CO O5~
rH 03 tO CO CD
OS to Tji t - CO CO
COtOOSCOOS OrHCOrH<
rHOStOCOCO rHrHtOrJtOO -rPCOCOCCtO OCNO Ol-- lO-fCOtOCO
oi c>5 oo oo co s d
OOCOOJCOOS OCNtOrHI
++ I ++ I + I ++
O 00 CO"CN CO OSO^ftOOO CNtOrHCOCO OSCOOO-^CO
XDCC rHCOCO o lOCNt^gJ rHCNl^COCO ^rHCOt^CD
+1+1+ T77++ TTTi+ ++TTT ++77+
CN (N CN CN CN
CO CO CO CO CO
28 39(1
lrH-^OSt>- rHCOOCNOS OrHC^ rr CN -^tOOSOCCN
COCNtOrH tOtOCNCOlO ^tOlOCOlO CNCOTfiTfilO
. CS CO CN t-H rH rO~-^ h- CO CO OS OS O
I 08(1
COCNtOrH lOiOrHCOtO GO I
"I AO N
^COt^-r^CN ddcO-^O ^COrHOrH
CN CN OCS
CO CO "9 U3
I -any
^4 r-I OJ OO
CO CO CO "3 C
rHI>. TJ1 CO CO
$$$$&
rHr-CSt^O OOrHt-O
t^ OCOt^iOCN CJStoOOscO t>-OOOOCOCO OcOt>-(
OrHOSrHtO CO CN OS OS, OS OS CO <
I udy
f OS 00 OO t- CN cb CO rH rj<
tOrHCC IOCOI>OCO
I O tOO O1OOSOO i
OrHTTitOO OrfitOCOO OOrHCOCNt^
iiOCNt^CO t^iOCOcO>O COI>.CSrHOC tocOOCOCN~
1-3-43^0005 cdoOrHcdco oscdosdcd coooocNrH
t- O CO rH t^- IO OS CO 00 CO CN~F^CN~O~tO OO^OO~O t- rH~
co So CN oTcN^to TJI oo coocTco ~CN"VO~
SO tO-^f rH
! 55S d c^^^^ 06
IrHCOCO O3OOSO3>O edl^todoO rHCOCOr)5<
ICNtOrH Tt^tOrHCNtO COTt<tOCO^ CNCO*^ 1 ^!
CO
:OOOrHrH rH
O O O I-H
>-l i-H (N CO
IO < CN CN TH
OrHCNCN CN
CN COCO^f
M^ liiii Illll
<1OOOO
CO CO COCO CO
EXTRACTS FROM NAUTICAL ALMANAC.
TABLE IV.
PROPORTIONAL PARTS.
253b
Interval
2 hours.
10
20
30
40
50
60
70
80
90
100
110
120
Interval
24 hours.
m
h m
1
1
1
1
2-
1
I
1
12
OA
3
1
1
1
2
2
2
2
ks
2
I
3
Z4
36
4
1
1
1
2
2
2
3
3
3
4
4
48
5
1
1
2
2
2
3
3
4
4
5
5
1
6
1
2
2
2
3
4
4
4
5
8
6
12
7
1
1
2
2
3
4
4
5
5
6
6
7
24
8
1
1
2
3
3
4
5
5
6
7
7
8
36
9
1
2
2
3
4
4
5
6
7
8
8
9
48
10
1
2
2
3
4
5
6
7
8
8
9
10
2
11
1
2
3
4
5
6
6
7
8
9
10
11
12
12
1
2
3
4
5
6
7
8
9
10
11
12
24
13
1
2
3
4
5
6
8
9
10
11
12
13
36
14
1
2
4
5
6
7
8
9
10
12
13
14
48
15
1
2
4
5
6
8
9
10
11
12
14
15
3
16
1
3
4
5
7
8
9
11
12
13"
15
16
12
17
1
3
4
6
7
8
10
11
13
14
16
17
24
18
2
3
4
6
8
9
10
12
14
15
16
18
36
19
2
3
5
6
8
10
11
13
14
16
17
19
48
20
2
3
5
7
8
10
12
13
15
17
18
. 20
4
21
2
4
5
7
9
10
12
14
16
18
19
21
12
22
2
4
6
7
9
11
13
15
16
18
20
22
24
23
2
4
6
8
10
12
13
15
17
19
21
23
36
24
2
4
6
8
10
12
14
16
18
20
22
24
48
25
2
4
6
8
10
12
15
17
19
21
23
25
5
26
2
4
6
9
11
13
15
17
20
22
24
26
12
27
2
4
7
9
11
14
16
18
20
22
25
27
24
28
2
5
7
9
12
14
16
19
21
23
26
28
36
29
2
5
7
10
12
14
17
19
22
24
27
29
48
30
2
5
8
10
12
15
18
20
22
25
28
30
6
31
3
5
8
10
13
16
18
21
23
26
28
31
12
32
3
5
8
11
13
16
19
21
24
27
29
32
24
33
3
6
8
11
14
16
19
22
25
28
30
33
36
34
3
6
8
11
14
17
20
23
26
28
31
34
48
35
3
6
9
12
15
18
20
23
26
29
32
35
7
36
3
6
9
12
15
18
21
24
27
30
33
36
12
37
3
6
9
12
15
18
22
25
28
31
34
37
24
38
3
6
10
13
16
19
22
25
28
32
35
38
36
39
3
6
10
13
16
20
23
26
29
32
36
39
48
40
3
7
10
13
17
20
23
27
30
33
37
40
8
41
3
7
10
14
17
20
24
27
31
34
38
41
12
42
4
7
10
14
18
21
24
28
32
35
38
42
24
43
4
7
11
14
18
22
25
29
32
36
39
43
36
44
4
7
11
15
18
22
26
29
33
37
40
44
48
Find the correction to be applied to the right ascension and declination of Jupiter on April 15, 1916, at
ll h 55 m 30 s a. m. local mean time, in Long. 81 15 W.
(Problem page 107.)
G.M.T.=15 d 5 h 20 m .5.
Difference of R. A. in 24 h =54. Difference for Dec. in 24 h =55.
With differences of 54 for R. A. and 55 for Dec. as arguments at top of page and the G. M. T. as argument
at right-hand side of page.
Corr. R. A., for 50; 5 h 12 m = 11 s Corr. Dec., for 50; 5 h 12 m = I .l
Corr. for 54= +0 S .8 Corr. for 55= -fOM
Corr. for 5 h 20 m .5= +0 S .3 Corr. for 5 h 20 m .5= O .O
Total
1M
Total
-f-0 .l +0 .l
R. A. (correction) -f!2M
Dec. (correction) +1/2
APPENDIX II.
A COLLECTION OF FOEMS FOE WOEKING DEAD BECKONING AND VAEI-
OUS ASTEONOMICAL SIGHTS, WITH NOTES EXPLAINING THEIB
APPLICATION UNDEE ALL OIECUMSTANCES.
(The figures in parenthesis refer to the Notes following these forms.)
FORM FOB DAY S WORK, DEAD RECKONING.
Time.
Compass Course.
Var.
Dev.
Lee
way.
Total
error.
True Course.
Patent
log.
Dist.
N.
S.
E.
W Difl.(i)
Long.
I
Latitude.
o /
Longitude.
Left at departure (or noon) (2) N. or S. (2) E. or W.
Run to. . . N. or S. E. or W.
By D. R. at
Run to
By D. R. at
N. or S.
N. or S.
N. or S.
E. or W.
E. or W.
E. or W.
FORM FOR TIME SIGHT OF SUN S LOWER LIMB (SUMNER LINE).
h. m. s.
W. T. . . ..
Obs. alt. Q
c-w +
Corr. .
Chro. t
h
C. C.
/ //
(io) G. M. T
( 3 ) S. D. +
( 6 )Eq. t.
(<)I. C. -t-
G. A. T.
+
/ //
dip - . ...
P& f
/ 1!
Corr. .. ..
O I If
h
Li
log sec
p
log cosec
2)
]
log cos
Si-h
log sin
h. m. s.
2)
GAT
L A.T.i
log sin 5 1
(h. m. s.~j
< T\ r ffntr . J IT? n
,* w
Dec.
H. D.
G. M. T.
Corr.
Dec.
N.orS.
N. or S.
( 8 )L,
Sfh
h. m. s.
G. A. T.
L. A.T.j
Eq. t.
H. D.
G. M. T.
Corr.
Eq. t.
log sec
log cosec
log cos
log sin
log sin i t t
(h. m. s.j
Long., lo "f"", ,\E.orW.
2)-
254
FORMS FOB WORK.
FORM FOB TIME SIGHT OF A STAB (SUMNEB LINE).
h. m. t.
255
W. T.
C-W +
Chro. t.
C.C.
(10) G. M. T.
R. A. M. S. +
Red. (Tab. 9) +
G. S. T.
R. A. *
(11) H. A. from Gr.
Obs. alt. *
Corr.
(<) I. C
dip
ref.
E. or W.
Corr.
h. m s.
R.A.
Dec.
N. or S.
2).
Gr. H. A.
( u ) H. A.,
h. m. 8.
log sec
log cosec
log cos
log sin
E. or W.
E. or W. log sin
( 8 ) Li
Sfh
Gr. H. A.
H.A.,
h. m. s.
log sec
log cosec
log cos
log sin
log sin h
2).
Long.i
h. m. s.
E. orW.
Long.
E. or W.
FOBM FOB TIME SIGHT OF A PLANET (SUMNEB LINE).
ft. m. s.
W.T.
C-W +.
Chro. t.
C.C.
. M. T.
R. A. M. S. + .
Red. (Tab. 9) +.
G. S. T.
R. A. *
Obs. alt. *.
Corr. .
(M) par. +.
( 4 ) I. C. +.
dip
(ii) H. A. from Gr E. or W. ref.
h. m. s.
R.A.
H. D. .
G. M. T
Corr. .
R. A.
h. m. 8.
Dec.
H.D. .
G. M. T
Corr. .
Dec.
.N. or S.
.X.orS.
Corr.
For the remainder of the work, by which the hour angles and thence the longitudes are found, employ the method
given under " Form for Time Sight of a Star (Sumner Line)."
61828 16 17
256
FORMS FOR WORK
FORM FOR TIME SIGHT OF MOON S LOWER LIMB (SUMNER LINE).
ft. 771. S. "in ^ m ^ g ^
W. T. Obs. alt. ( ( 16 ) R. A. 0)
Dec. N orS.
c-w +.. ~
Chro. t. . ()S.D 4- H. D. +
H. D.
C. C. . Aug 4- TO.
fn
(*)I.C. 4- - G.M.T.
G.M.T.
(10\ P \T T
R.A.M.S. + + ... *.
, ,,
Red. (Tab. 9)4- - Corr.
Corr
G. S. T. dip ft. m. s
/ II
Dec. N or S
i a
(") H A from Gr E orW 1st corr ( 5 )
Approx. alt.
p & r (Tab 24)4-
-
h
For the remainder of the work, by which the hour angles and thence the longitudes are found,
under "Form for Time Sight of a Star (Sumner Line)."
FORM FOR MERIDIAN ALTITUDE OF SUN S LOWER LIMB.
" " ft. m..
Obs. alt. ... ( 3 ) S. D. +. ... L. A. T.
employ the method given
Dec N or S.
Corr. ( 4 ) I.C. 4- Long.
h 4- G.A.T. .
H.D.
h.
/ // t It
( 17 ) z N or S dip GMT
d N.orS. p. & r.
i n
_
Lat. N.orS. -
1 II
Dec. N or S
Corr. .
FORM FOR MERIDIAN ALTITUDE OF A STAR.
Obs.alt. * (4) i.e. +
Dec. N. or S.
Corr. .
h din
< ref.
d N.orS. -
Lat. .. N.orS. "
Corr.
FORM FOR MERIDIAN ALTITUDE OF A PLANET.
" " h. m.
Obs. alt. ^< . ( 14 ) par 4- G M T Gr trans
1 II
Dec N or S
Corr. ( 4 ) I.C. + Corr. for Long.
lt
ft + . L M T localtrans.
H.D.
ft.
. o r n i it
GMT
d N.orS. ref.
1 !
Lat. N.orS. -.
Dec. ...N.orS.
Corr.
(")*
d
FORMS FOR WORK.
FORM FOR MERIDIAN ALTITUDE OF MOON S LOWER LIMB.
Obs. alt.
257
h. m.
G. M. T., Gr. trans. ( ie )Dec.
Corr. for Long. (Tab. 11)
N.orS. ()S.D.
N. or S. Aug.
()I. C.
N. or S.
dip
1st corr
Approx. Alt.
p.<frr.(Tab.24)
L. M. T., local trans.
Long.
G. M. T.. local trans.
H. D. .
G.M.T. .
Cora. .
m
Dec.
N.orS.
ALTERNATIVE FORM FOR MERIDIAN ALTITUDE OF A BODY. ()
90 00 00" Rules for tignt.
Corr.
Constant
Obs. Alt.
Lat.
W. T.
C-W
Chro. t.
C. C.
(") G. M. T.
() Bq. t.
G. A. T.
Long.i
Case I Lat <fe Dec same name Lat greater . ... +90"+Dec Corr Alt
Case II Lat & Dec same name Dec greater 90+Dec +Corr ^Alt
Case III Lat and Dec. opposite names +90 Dec. Corr Alt
Case IV Lower tran^ o-oo . r><v j-Pni^ a. Ait
N. or S.
FORM FOR LATITUDE SIGHTS OF SUN S LOWER LIMB (SUMNEB LINE).
h. m. s. " ** " m, 9.
Obs. alt. Q Dec. N.orS. TCn. t
Corr.
H. D. 4- H.D.
h
h. h.
G.M.T G.M T
m s D -f
" t.
(*) I. C. +..
4-
" m. *
Dec N.orS. Eq. t. .
/ n
L. A. T.i
PO*
(*) Long.,
L.A.T.I
k
i
ti
o &r
*
Reduction to Meridian,
it
(**) a
" TTT
Corr i
^B
h. m. s.
h. m. s.
/ //
<t> 4>" Method.
//
log sec
d
log tan log cosec .
i a t a
h h
()9>i"
...N.orS. log tan log sin
(*)a*i afj*
T
Hi H
91
^o"^^T^ e / //
Lat.j
...N.orS.
C /
tt
( 17 ) z\ N.orS. z*
d N or S d
Lat.i N.orS. Lati N.orS.
h
log sin
94
N or S log tan log sin
pi*
...N.orS. log cos
I^t..~
V nr S
258
FORMS FOE WORK.
FORM FOB LATITUDE SIGHTS OF A STAB (SUMNEB LINE).
h. m. s.
W.T.
c-w +
Chro. t.
C. C.
(10) G. M. T.
R. A. M. S. +
Red.(Tab.9) +
G. S. T.
R. A.*
(11) H. A.fromGr E.orW.
(*) Long.i E.orW.
h. m. s.
(si) Long. 2
h. m. s.
h. m. s.
E.orW.
E.orW.
E. or W.
Obs.alt.* .
Corr. .
h
dip
ref.
Corr. .
h. m. s.
R.A.
Dec.
N.orS.
For the remainder of the work, by which the latitudes are found from either the <p <p" formula or the reduction to the
meridian, employ the methods given under " Form for Latitude Sights of Sun s Lower Limb (Sumner Line) ."
FOBM FOB LATITUDE SIGHTS OF A PLANET (SUMNEB LINE).
h. m. s.
W.T.
c-w +.
Chro. t.
C. C. .
. M. T.
R.A. M.S. +.
Red.(Tab.9) +.
G. S. T.
R. A.*
h. m. s. "
Obs.alt.:>|c R.A. Dec. N.orS.
a. r"*" 1 "
h H.D. H.D.
" G. M. T G. M. T
(M)par. +
(*) I.C. + *.
( n ) H. A. from Gr
() Long.!
h. m. s.
E.orW.
dip -.
E.orW. ref. -.
E. or W.
Corr. .
h. m. s.
o r ff
R.A,
Dec.
N.orS.
("-I) Long.a
h. m. s.
E.orW.
E.orW.
For the remainder of the work, by which the latitudes are found from either the <p <?" formula or the reduction to the
meridian, employ the methods given under " Forms for Latitude Sights of Sun s Lower Limb (Sumner Line)."
FORMS FOE WORK.
FORM FOB LATITUDE SIGHTS OF MOON S LOWER LIMB (StJMNER LINE).
h. m. 8.
W.T.
C-W +
Chro. t.
C. C.
() G. M.T.
R. A. M. 8. +
Red. (Tab. 9) -f
G. S. T.
R.A.C
() H. A. from Gr E.orW.
() Long.i E.orW.
h. m. t.
() S. D.
Aug.
dip
h. TO. *.
Long.,
E. or W.
E.orW.
1st Corr.
Approx. alt.
p. &r. (Tab. 24)
P) R. A.
(") Dec.
H.D. + H.D.
m.
G.M.T. G.M.T.
Con.
R. A.
h. m. i.
259
.N.orS.
Corr.
Dec.
h. TO. *. I
"o"i",i "[E.OTW.
For the remainder of the work, by which the latitudes are found from either the 9 <p" formula or the reduction to the
leridian, employ the methods given under " Forms for Latitude Sights of Sun s Lower Limb (Sumner Line)."
FORM FOR FINDING THE TIME OF HIGH (OR LOW) WATER.
d. h. m.
G. M. T. of Greenwich transit
Corr. for Long. (Tab. 11)
L. M. T. of local transit
Lunitidal int. (App. IV)
L. M. T. of high (or low) water
260
FORMS FOE WORK.
FORM FOB FINDING THE CALCULATED ALTITUDE AND THE ALTITUDE DIFFERENCE FOR LAYING DOWN THE
SUMNER LINE BY THE METHOD OF SAINT HILAIRE FROM A SIGHT OF THE SUN S LOWER LIMB.
(SINE COSINE FORMULAE)
h. m. s.
W. T.
Dec. . N. or8. Eq. t.
c-w +
g
- II D n D
Chro. t.
A.
A.
C C
GMT G. M T
( 10 ) G. M. T.
Corr . . Corr.
j.
(6) Eq. t.
^^7^"""^"
G. A. T.
d 4_; Eq. t.
T
Long, of assumed Pos.
E. or W.
L. A. T.-
A. TO. S. "
log cos
"
L ah log sin ... -t log cos
Obs. alt. Q
o / n
d i log sin .... i log cos
<*
1C 4-
(Sum) log A dr log B .
-
Corr. (Tab. 46)
A B
Obs h
A ... .
Calculated h
nat. sin A 4- B
Alt. Diff
FORM FOR FINDING THE
SUMNER LINE BY T
W. T.
CALCULATED ALTITUDE AND THE ALTITUDE DIFFERENCE FOR LAYING
HE METHOD OF SAINT HILAIRE FROM A SIGHT OF THE SUN S LOWER
(COSINE HAYERSINE FORMULA.*)
h.m.s. " w.
Dec. . . N. or S. Eq. t. . . .
DOWN TH1
LIMB.
*.
C W. + .
H. D.
"J 1
H D db
Chro. t
.. . A
A.
C C d;
GMT G M. T
//
(io) GMT
Corr -t- Corr.
C 6 ) Eq t
m
GAT
d 4- Ea t
Long, of as-\ .
E or W
L. A. T.=-<
A. m. s.
log hav Obs alt Q
//
L
O / ft
log cos I. C. +
d
log cos Corr. (Tab. 46).
log hav 9 (Sum) Obs A
nat hav 9 1 Calculated A
T rt
nat hav Alt Diff.
-
nat hav (Sum)
Calculated A \
=90 3 >
1 Sine cosine formula: sin A =sin L sin d -f cos L cos d cos t
A + B
2 Cosine haversine formula: hav s =har (L~d) + cos L cos d hav t
=hav (L~d) + hav 9
FORMS FOE WORK.
261
FOBM FOB FINDING THE CALCULATED ALTITUDE AND THE ALTITUDE DIFFERENCE FOB LAYING DOWN THE
SUMNEB LINE BY THE METHOD OF SAINT HILAIBE FBOM A SIGHT OF THE SUN S LOWEB LIMB.
("MHAVEBSINE FORMULA. )
h. TO. 8.
W T
Dec. N or S. Eq t
C W -f .
1
Chro t
H. D. -J- . H D i
c c
h h
G. M. T. GMT
() G. M. T.
C) Ea t ..
in .
Pnrr 4- COIT 4-
GAT
Long of as- 1
m. s.
E. or W. Dec N orS Eq t
sumed Pos. /
L. A T. i
t It
H
(*)P. D. ....
co. L.
coL-f-PD nat hav
co L. P.D. nat hav ....
nat hay A ... (Diff 4
log hav A .. \
log hay t /
" log hay B (Sum)
Obs Alt Q nat hav B
1C + nat hav (co L P D ) /
Corr. (Tab. 46) of >...-. /c\
Obs h "
Calculated h z .
Alt. Diff. Calculated h\
FOBM FOB FINDING THE CALCULATED ALTITUDE AND THE ALTITUDE DIFFERENCE FOB LAYING DOWN
THE SUMNEB LINE BY THE METHOD OF SAINT HILAIBE FBOM A SIGHT OF A STAB.
(SINE-COSINE FORMULA.*)
h. m. s.
C-W -f
I. C. -f . . ..
______
Corr. (Tab. 46)
A. T7l. S
R V
c c.
Obs. h
______
(io\ GMT
o / //
t
log cos i
RAMS +
L i log sin i
Red (Tab 9) +
d i log sin i
log cos
GST
(Sum) log A ... i
log B i
R A *
A
B . .
/ H
A_i_
( ll ) H A 3k from Gr E or W
Calculated h
( s ) Long of assumed Pos E or W
Obs h
.
1 7 "
Alt Diff nat sin= A-f B
jo/ n
V
1 Haversine formula: hav z = {hay (co. L + P. D.) hav (co. L P.D.)>hav t + hav (co. L P.D.)
= hav B + hav (co.L P.D.) ; where hav B=hav A hav t, and hav A=hav (co.L+
P. D.)-hav (co. L P. D.)
Sine cosine formula: sin h =sin L sin d + cos L cos d cos t
A + B
i
262
FORMS FOB WORK.
FORM FOB FINDING THE CALCULATED ALTITUDE AND THE ALTITUDE DIFFERENCE FOR LAYING DOWN THE
SUMNER LINE BY THE METHOD OF SAINT HILAIRE FROM A SIGHT OF A STAR.
h. m. s.
(COSINE-HAVERSINE FORMULA. 1 )
h. m. s.
W. T.
t ...
. . . log hav
Dec. (d)
C-W +
o /
L
//
log cos
h. m. s.
R. A.
Chro t
d
log cos
TT
C C
log hav 6 (Sum )
Of//
Obs alt *
(io) GMT
nat hav 6 ........"i
1C +
RAMS +
L~d
... nat hav /
Corr. (Tab 46)
Red (Tab 9)+
z . . .
... nat hav (Sum)
Obs. h
G. S T.
R. A.*
Calcu- ^
latedft J
//
.... =90-z
(") H. A. * \ E orW
from Gr. i
C 25 ) Long, of \ EorW.
Alt. diff
assumed PosJ
t
N. orS.
FORM FOR FINDING THE CALCULATED ALTITUDE AND THE ALTITUDE DIFFERENCE FOB LAYING DOWN
THE SUMNER LINE BY THE METHOD OF SAINT HILAIRE FROM A SIGHT OF A STAB.
h. m. s.
() (HAVERSINE FORMULAE)
O / //
h. m. g.
W T
. Dec. N. or S.
R A
C W +
(6) P. D.
Chro. t.
... co. L.
o / //
Obs. alt *
C C ...
co. L+P. D nat hav
I. C +
(io) G M. T.
. .. co. L P. D nat hav
Corr (Tab 46)
R. A. M. S. + .
. ... nat hav A
... (Diff.) Obs h
Red.(Tab.9)+
loghavA
1 Calculated h
G. S. T.
h. m. s.
.. t ........ log hav
AH. diff.
R A #
log hav B
(Sum)
(") H.A. sjcfronn
Gr J
E or W nat hav B
1"
(25) Long, of as- \
sumed Pos /
/ /
E. or W. co L P D nat hav
I
z nat hav
(Sum)
O 1 It
Calculated h 1
=90- z f
i Cosine haversine formula: hav z =hav (L~d) + cos L cos d hav t
=hav (L~d) + hav d
> Haversine formula: hav 2 = {hav (co. L + P. D.) hav (co. L-P. D.)} hav t + hav (co. L-P. D.)
= hav B + hav (co. L P. D.); where hav B=hav A hav t, and hav A=hav (co. L+
P. D.)-hav (co. L-P. D.)
FORMS FOR WORK.
263
FORM FOR FINDING THE CALCULATED ALTITUDE AND THE ALTITUDE DIFFERENCE FOB LAYING
DOWN THE SUMNER LINE BY THE METHOD OF SAINT HILAIRE FROM A SIGHT OF A PLANET.
ft. m. s.
W.T.
C-W +.
Chro. t.
C. C. ,
(") G. M. T.
R.A. M. S.-f.
Red.(Tab.9)+.
G.S.T.
R.A.*
R.A.
H. D.
G. M. T.
Corr.
R. A.
Gr.
.E. orW.
(*) Long, of as-\
surned Posj E. or W.
(SINE-COSINE FORMULA )
ft. m. s.
Calculated h
Dec.
N. or S.Obs. alt.
a.
H D
1C +
ft.
GMT
ft.
Corr (Tab 46)
Corr.
.... Obs. ft
d
-j. Calculated ft
Alt. Diff . .
O 1 II
log cos i
. . . . . log sin ...
4j log COS
.......... log sin ....
- log COS . ...
(Sum) log A
4- log B 4-
A ...
B
m t II
A
=A+B
FORM FOR FINDING THE CALCULATED ALTITUDE AND THE ALTITUDE DIFFERENCE FOR LAYING
DOWN THE SUMNER LINE BY THE METHOD OF SAINT HILAIRE FROM A SIGHT OF A PLANET.
(COSINE-HAVERSINE FORMULA.*)
h. m. e. h. m. s. h. m, f. "
C-W -f ... .
O 1
L
log cos H. D. 4-...
s. "
H. D.
Chro. t.
d
... log cos . G. M T.
h. h.
G. M. T
C C
log hav B (Sum) Corr i
Corr
no) GMT
nat hav 6 \ R A
d 4-
R.A M.S. -f
L^d
... nat hav . . /
Red.(Tab.9)+
... 2 ....
nat hav (Sum)
G.S.T.
/
//
Obs alt.
Calcu- \
I. C. -f. ..
R. A. ^c
lated/U
,=90_ 2
Corr. (Tab. 46)
fu) tl. A. 5|<f rom^
Gr. /
E. orW.
Obs h
() Long, of as-\
pnmpfl Pop.)
E. or W.
Calcu- i
lated hi
f
Alt. Diff.
1 Sine cosine formula: sin ft =sin L sin d + cos L cos d coe t
A + B
* Cosine haversine formula: hav z =hav (L~<i) -f cos L cos d hav t
=hav (L~d) + hav 6
264
FOEMS FOR WORK.
FORM FOB FINDING THE CALCULATED ALTITUDE AND THE ALTITUDE DIFFERENCE FOB LAYING DOWN THE
SUMNER LINE BY THE METHOD OF SAINT 111 LA IRK FROM A SIGHT OF A PLANET.
h. TO. 8.
() (HAVERSINE FORMULA.) 1
o / n
C-W + .
n
H. D
co. L P. D nat hav
Chro. t.
h
G. M. T.
nat hav A. .
(Diff.)
C. C.
log hav A
~ L ~
( M ) G M. T*
/ //
Dec
A. TO. *.
N. or S. t log hav
R A. M S. +
(*) P. D
log hav B
Sunn
Red. (Tab. 9) +
nat havB.
G. 8. T
o / n
co. L + P.D
O / /f
co. L P. D nat hav
R. A. *
co.L-P.D
s nat hav
Sum)
( u ) H A sfcfromGr. ...
h. m. 8.
. E. or W. R.A.
(*) Long, of AS-\
sumed Pos /
^^
s.
E or W H D
1 II f ft
Calculated h\ Obs alt
t
h.
G.M.T.
=90 z /
Obs h I +
8.
Corr
Corr.-\
Alt Diff (Tab 46 w
h. TO. S.
R A
Obs h
Haversine formula: hav z - -{hav (co. L + P. D.)- hav (co. L-P. D.)} hav t + hav (co. L-P. D.)
hav B -f hav (co. L P. D.); where hav B=hav A hav t, and hav A hav (co. L4-
P. D.)-har (co. L-P. D.)
FORMS FOR WORK. 265
NOTES RELATING TO THE FORMS.
1 . It is not necessary to convert departure into difference of longitude for each course; it will suffice to make one conversion for
the sum of all the departures used in bringing forward the position to any particular tune.
2. In D. R. it will be found convenient to work Lat. and Long, in minutes and tenths, rather than in minutes and seconds.
3. If upper limb is observed, the correction for S. D. should be negative, instead of positive.
4. A positive I. C. has been assumed for illustration throughout the forms; if negative, it should be included with the mintu
terms of the correction.
5. To obtain p, subtract Dec. from 90 if of same name as Lat.; add to 90 if of opposite name
fi. Sign of Eq. t. that of application to mean time.
7. If G. A. T. is later than L. A. T., Long, is west; otherwise it is east.
8. If Lat. is exactly known, a second latitude need not be employed.
9. s andr- & may be obtained by applying half the difference between LI and L 2 with proper sign, to i and i h , respectively.
10. The G. M. T. must represent the proper number of hours from noon, the beginning of the astronomical day; to obtain this
it may be necessary to add 12*> to the Chro. t.
11. H. A. from Greenwich is the difference between G. S. T. and R. A., and should be marked W. if the former is greater:
otherwise, E.
12. Local H. A. is marked E. or W., according as the body is east or west of the meridian at time of observation.
13. Subtract local hour angle from Greenwich hour angle to obtain longitude; that is, change name of local hour angle and
combine algebraically.
14. The forms include a correction for the parallax of a planet, but in most cases this is small, and may be omitted. When
used, take hor. par. from Naut. Aim. and reduce to observe altitude by Table 17. The semidiameter of a planet may be disregarded
in sextant work if the center of the body is brought to the horizon line.
15. If upper limb is observed, the corrections for S. D. and Aug. should be negative, instead of positive.
16. R. A. and Dec. are to be picked out of Naut. Aim. for nearest hour of G. M. T. , and to be corrected for the number of minutes
and tenths.
17. Mark zenith distance N. or S. according as zenith is north or south of the body observed; mark Dec. according to its name,
subtracting it from 180 for cases of lower transit; then, in combining the two for Lat., have regard to their names.
18. This form enables "Constant " to be worked up before sight is taken, and gives latitude directly on completion of meridian
observation. Longitude and altitude at transit must be known in advance with sufficient accuracy for correcting terms.
19. The details of obtaining Dec. at transit and correction for altitude are shown in the meridian altitude forms for each of the
various bodies.
20. In an a. m. sight subtract L. A. T. from 24> to obtain t; in a p. m. sight L. A. T. is equal to t .
21. If Long, is exactly known, a second longitude need not be employed.
22. Mark <" N. or S. according to name of Dec., and subtract it from ISO when body is nearer to lower than to upper transit;
mark <t> N. or S. according as zenith is north or south of the body; then combine for Lat. having regard to the names
23. Take a from Table 26 and af from Table 27.
24. Add for upper, subtract for lower transits.
25. Subtract longitude from Greenwich hour angle to obtain local hour angle; that is, change name of longitude and combine
algebraically.
26. Add for west, subtract for east longitude.
27. As the trigonometric functions are all haversines in this solution, the abbreviation, hav, might be omitted, and the abbre
riations, nat. and log, might be employed to indicate the natural haversine and the log haversine, respectively.
APPENDIX III.
EXPLANATION OF CERTAIN EULES AND PRINCIPLES OF MATHEMATICS
OF USE IN THE SOLUTION OF PROBLEMS IN NAVIGATION,
DECIMAL FRACTIONS.
Fractions, or Vulgar Fractions, are expressions for any assignable part of a unit ; they are usually
denoted by two numbers, placed one above the other, with a line between them ; thus i denotes the
fraction one-fourth, or one part out of four of some whole quantity, considered as divisible into four
equal parts. The lower number, 4, is called the denoniinator of the fraction, showing into how many
parts the whole is divided ; and the upper number, 1, is called the numerator, and shows how many of
those equal parts are contained in the fraction. It is evident that if the numerator and denominator be
varied in the same ratio the value of the fraction will remain unaltered ; thus, if both the numerator
and denominator of the fraction J be multiplied by 2, 3, 4, etc., the fractions arising will be f, T \, -^,
etc., all of which are evidently equal to J.
A Decimal Fraction is a fraction whose denominator is always a unit with some number of ciphers
annexed and the numerator any number whatever ; as &, y^, -j-Jthr, etc. And as the denominator of
a decimal is always one of the numbers 10, 100, 1000, etc., the necessity for writing the denominator,
may be avoided by employing a point ; thus, -^ is written .3, and -^ is written .14 ; the mixed number
3^, consisting of a whole number and a fractional one, is written 3.14.
In setting down a decimal fraction the numerator must consist of as many places as there are
ciphers in the denominator ; and if it has not so many figures the defect must be supplied by placing
ciphers before it ; thus, -^=.16, T ^f Tr =.016, Tinnn7 == - 0016, etc. And as ciphers on the right-hand side
of integers increase their value in a tenfold proportion, as 2, 20, 200, etc., so when set on the left handx
of decimal fractions they decrease their value in a tenfold proportion, as .2, .02, .002, etc. ; but ciphers
set on the right hand of these fractions make no alteration in their value; thus, .2 is the same as
.20 or .200.
The common arithmetical operations are performed the same way in decimals as they are in inte
gers, regard being had only to the particular notation to distinguish the integral from the fractional
part of a sum.
ADDITION OP DECIMALS. Addition of decimals is performed exactly like that of whole numbers,
placing the numbers of the same denomination under each other, in which case the separating decimal
points will range straight in one column.
EXAMPLES.
Miles. Feet. Inches.
Add: 26.7 1.26 272.3267
32. 15 2. 31 . 0134
143. 206 1. 785 2. 1576
.003 2.0 31.4
Sum: 202.059 7.355 305.8977
SUBTBACTION OP DECIMALS. Subtraction of decimals is performed in the same manner as in whole
numbers, observing to set the figures of the same denomination and the separating points directly
under each other.
EXAMPLES.
From: 31.267 36.75 1.254 1364.2
Take: 2.63 .026 .316 25.163
Difference: 28.637 36.724 .938 1339.037
MULTIPLICATION OF DECIMALS. Multiply the numbers together as if they were whole numbers,
and point off as many decimals from the right hand as there are decimals in both factors together ; and
when it happens that there are not so many figures in the product as there must be decimals, then
prefix such number of ciphers to the left hand as will supply the defect.
EXAMPLE I. EXAMPLE II.
Multiply 3. 25 by 4. 5
3.25
4.5
Answer : . 0102
Answer : 14. 625
1625
1300
In one of the factors is one decimal, and in the
other two ; their sum, 3, is the number of decimals
of the product.
266
Multiply . 17 by .06
.17
.06
In each of the factors are two decimals; the pro
duct ought therefore to contain 4 ; and, there being
only three figures in the product, a cipher must be
prefixed.
RULES AND PRINCIPLES OF MATHEMATICS.
267
EXAMPLE III.
Multiply 0.5 by 0.7
0.5
0.7
Answer:
0.35
EXAMPLE IV.
Multiply .18 by 24
Answer:
4.32
DIVISION OF DECIMALS. Division of decimals is performed in the same manner as in whole num
bers. The number of decimals in the quotient ^ must be equal to the excess of the number of decimals
of the dividend above those of the divisor; when the divisor contains more decimals than the dividend,
ciphers must be affixed to the right hand of the latter to make the number equal or exceed that of the
divisor.
EXAMPLE I.
Divide 14.625 by 3.25
3.25)14.625(4.5
13 00
1625
1625
In this- example there are two decimals in the
divisor and three in the dividend; hence, there is
one decimal in the quotient.
EXAMPLE II.
Divide 3.1 by .0062
Previous to the division affix three ciphers to
the right hand of 3.1, to make the number o-f deci
mals in the dividend equal the number in the
divisor.
.0062)3.1000(500
3 10
000
EXAMPLE III.
Divide 17.256 by 1.16
1.16)17.25600(14.875+
11 6
565
464
1016
928
880
812
680
580
100
By pursuing the operation further the quotient
may be carried out as many decimal places as
desired.
MULTIPLICATION OF DECIMALS BY CONTRACTION. The operation of multiplication of decimal fractions
may be very much abbreviated when it is not required to retain any figures beyond a certain order or
place; this will constantly occur in reducing the elements taken from the Nautical Almanac from Green
wich noon to later or earlier instants of time.
In multiplying by this method, omit writing down that part of the operation which involves
decimal places below the required order, but mental note should be made of the product of the first
discarded figure by the multiplying figure, and the proper number of tens should be carried over to
insure accuracy in the lowest decimal place sought.
EXAMPLE: Required the reduction for the sun s decimation for 7 h .43, the hourly difference being
58". 18, where the product is required to the second decimal.
By ordinary method.
58".18
7 h .43
17454
23272
40726
432".2774
By contraction.
58". 18
7 h .43
1.74
23.27
407.26
432."27
In the contracted method, for the multiplier .03 it is not necessary to record the product of any
figures in the multiplicand below units; for the multiplier .4, none below tenths; but in each case
.observe the product of the left-hand one of the rejected figures and carry forward the number of tens.
268
RULES AND PRINCIPLES OF MATHEMATICS.
RULES AND PRINCIPLES OF MATHEMATICS.
REDUCTION OP DECIMALS. To reduce a vulgar fraction to a decimal, add any number of ciphers to
the numerator and divide it by the denominator; the quotient will be the decimal fraction. The decimal
point must be so placed that there may be as many figures to the right hand of it as there were added
ciphers to the numerator. If there are not so many figures in the quotient place ciphers to the left hand
to make up the number.
EXAMPLE I.
Reduce ^ to a decimal.
50)1.00
.02 Answer.
EXAMPLE II.
Reduce f to a decimal.
8)3.000
.375 Answer.
EXAMPLE III.
Reduce 3 inches to the decimal of a foot.
Since 12 inches=l foot this fraction is -j^.
12)3.00
.25 Answer.
EXAMPLE IV.
Reduce 15 minutes to the decimal of an hour.
Since 60 m = l h , this fraction is $.
60)15.00
.25 Answer.
EXAMPLE V.
Reduce 17 m 22 f to the decimal of an hour.
22 m
22- = =0 m .37.
60
17 h .37
17=i 37 = =0 h .289-f Answer.
Any decimal may be reduced to lower denominations of the same quantity by multiplying it by the
number representing the relation between the respective denominations.
EXAMPLE VI. Reduce 7.231 days to days, hours, minutes, and seconds.
32 m .640
O m .640
60
38". 400
Answer: 7 d 5 h 32 m 38.4.
5 h .544
GEOMETRY.
Geometry is the science which treats of the description, properties, and relations of magnitudes, of
which there are three kinds; viz, a line, which has only length without either breadth or thickness; a
surface, comprehended by length and breadth; and a solid, which has length, breadth, and thickness.
A point, considered mathematically, has neither length, breadth, nor thickness; it denotes position
simply.
A line has length without breadth or thickness.
A surface has length and breadth without thickness.
A solid has length, breadth, and thickness.
A straight or right line is the shortest distance between two points on a plane surface.
A plane surface is one in which, any two points being taken, the straight line between them lies
wholly within that surface.
Parallel lines are such as are in the same plane and if extended indefinitely never meet.
A circle is a plane figure bounded by a curved line of which every point is
equally distant from a point within called the center. The bounding curve of
the circle is called the circumference.
The radius of a circle, or semidiameter, is a right line drawn from the
center to the circumference, as AC (fig. 82); its length is that distance which
is taken between the points of the compasses to describe the circle.
A diameter of a circle is a right line drawn through the center and termi-
fjs nated at both ends by the circumference, as ACB, its length being twice that
of the radius. A diameter divides the circle and its circumference into two
equal parts.
An arc of a circle is any portion of the circumference, as DFE.
The chord of an arc is a straight line joining the ends of the arc. It divides
the circle into two unequal parts, called segments, and is a chord to them both;
thus, DE is the chord of the arcs DFE and DGE.
A semicircle, or half circle, is a figure contained between a diameter and the arc terminated by that
diameter, as AGB or AFB.
FIG. 82.
RULES AND PRINCIPLES OF MATHEMATICS. 269
Any part of a circle contained between two radii and an arc is called a sector, as GCH.
A quadrant is half a semicircle, or one-fourth part of a whole circle, as CAG.
All circles are supposed to have their circumferences divided into 360 equal parts, called degrees;
each degree is divided into 60 equal parts, called minutes; and each minute into 60 equal parts, called
seconds; an arc is measured by the number of degrees, minutes, and seconds that it contains.
A sphere is a solid bounded by a surface of which every point is equally distant from a point within,
which, as in the circle, is called the center. Substituting surface for circumference, the definitions of the
radius and diameter, as given for the circle, apply for the sphere.
An angle is the inclination of two intersecting lines, and is measured by the arc of a circle inter
cepted between the two lines that form the angle, the center of the circle being the point of intersection.
A right angle is one that is measured by a quadrant, or 90. An acute angle is one which is less than
a right angle. An obtuse angle is one which is greater than a right angle.
A plane triangle is a figure contained by three straight lines in the same plane.
When the three sides are equal, the triangle is called equilateral; when two of them are equal, it is
called isosceles. When one of the angles is 90, the triangle is said to be right-angled. When each angle
is less than 90, it is said to be acute-angled. When one is greater than 90, it is said to be obtuse-angled.
Triangles that are not right-angled are generally called oblique-angled.
A quadrilateral figure is one bounded by four sides. If the opposite sides are parallel, it is called a
parallelogram. A parallelogram having all its sides equal and its angles right angles is called a square.
When the angles are right angles and only the opposite sides equal, it is called a rectangle.
In a right-angled triangle the side opposite the right angle is called the hypotenuse, one of the other
rides is called the base, and the third side is called the perpendicular. In any oblique-angled triangle,
one side having been assumed as a base, the distance from the intersection of the other two sides to the
base or the base extended, measured at right angles to the latter, is the perpendicular. In a parallelo
gram, one of the sides having been assumed as the base, the distance from its opposite side, measured
at right angles to its direction, is the perpendicular. The term altitude is sometimes substituted for
perpendicular in this sense.
Every section of a sphere made by a plane is a circle. A great circle of a sphere is a section of the
surface made by a plane which passes* through its center. A small circle is a section by a plane which
intersects the sphere without passing through the center.
A great circle may be drawn through any two points on the surface of a sphere, and the arc of that
circle lying between those points is shorter than any other distance between them that can be measured
upon the surface. All great circles of a sphere have equal radii, and all bisect each other.
The extremities of that diameter of the sphere which is perpendicular to the plane of a circle are
called the poles of that circle. In the case of a small circle the poles are named the adjacent pole and
the remote pole. All circles of a sphere that are parallel have the same poles. All points in the circum
ference of a circle are equidistant from the poles. In the case of a great circle, the poles are 90 distant
from every point of the circle.
Assuming any great circle as a priinary, all great circles which pass through its poles are called its
secondaries. All secondaries cut the primary at right angles.
USEFUL FORMULAE DERIVED FROM GEOMETRY. In these formulae the following abbreviations are
adopted:
6, base of triangle or parallelogram. r, radius of sphere or circle.
h, perpendicular of triangle or parallelogram. d, diameter of sphere or circle.
/, height of cylinder or cone. A, major axis of ellipse.
it, ratio of diameter to circumference a, minor axis of ellipse.
( = 3. 141593 ) . s, side of a cube.
Area of parallelogram = b X h.
Area of triangle = b X h.
Area of any right-lined figure = sum of the areas of the triangles into which it is divided.
Sum of three angles of any triangle = 180.
Circumference of circle = 2?rr, or ltd.
Tfd 2
Area of circle = nr*, or -7-.
Angle subtended by arc equal to radius = 57. 29578.
ird?
Volume of sphere = ~~g~
Surface of sphere = nd 2 , or 4irr*.
t 11- *^ a
Area of ellipse = ^ .
Volume of cube = s 3 .
Volume of cylinder = Area of base X I.
Volume of pyramid or cone = Area of base X IT.
f JVLJL-N VJ.jr.L,.Cja
-, or Pe
c h
rpendicular
ypotenuse
. g
TRIGONOMETRIC FUNCTIONS.
The trigonometric functions of the angle formed by any two lines
are the ratios existing between the sides of a right triangle formed by
letting fall a perpendicular from any point in one line upon the
other line; no matter what point is chosen for the perpendicular
nor which line, the ratios, and therefore the respective functions,
will be the same for any given angle.
Let ABC (fig. 83) be a plane right triangle in which C is the
right angle: A and B, the other angles; c, the hypotenuse; a and
6 the sides opposite the angles A and B, respectively. In considering
the functions of the angle A, its opposite side, a, is regarded as the
perpendicular, and its adjacent side, 6, as the base; for the angle B, 6
is the perpendicular and a the base. Then the various ratios are
designated as follows:
Qf the Je A abbreviated sin A;
, is called the cosine of the angle A, abbreviated cos A;
, ,
c hypotenuse
a or perpendicular ig called ^ t ent of the ang]e A abbreviated tan A;
b base
, is called the cotangent of the angle A, abbreviated cot A;
i, or-
a perpendicular
or
. > is called the secant of the angle A, abbreviated sec A;
.
or Jw otenus L, is called the cosecant of the angle A, abbreviated cosec A;
a perpendicular
1 cosine A, is called the versed sine of A, abbreviated vers A.
1 sine A, is called the co-versed sine of A, abbreviated covers A.
(1 cosine A) is called the haversine of A, abbreviated hav A.
The following relations may be seen to exist between the various functions:
1
sin A
6 c
= 1 -*-- = -*- = sec A;
cos A
sin A a b
Hence the cosecant is the reciprocal of the sine, the secant is the reciprocal of the cosine, the cotan
gent is the reciprocal of the tangent, and the tangent equals the sine divided by the cosine.
The complement of an angle is equal to 90 minus that angle, and thus in the triangle ABC the
angle B is the complement of A. The supplement is equal to 180 minus the angle.
From the triangle ABC, regarding the angle B, we have:
sin B = = cos A;
C
tan B = = cot A;
sec B = = cosec A<
RULES AND PRINCIPLES OF MATHEMATICS.
271
Hence it may be seen that the sine of an angle is the cosine of the complement of that angle; the
tangent of an anjjle is the cotangent of its comple
ment, and the secant of an angle is the cosecant of
its complement.
The functions of angles vary in sign according
to the quadrant in which the angles are located.
Let A A and BB X (fig. 84) be two lines at right
angles intersecting at the point O, and let that point
be the center about which a radius revolves from
an initial position OB, successively passing the points
A, B , A . In considering the angle made by this
radius at any position, P , P", P ", P //x/ , with the
line OB, its position of origin, the functions will
depend upon the ratios existing between the sides
of a right triangle whose base, 6, will always lie
within BB / , vnd whose perpendicular, a, will always
be parallel to A A , while its hypotenuse, c (of a con
stant length equal to that of the radius), will de
pend upon the position occupied by the radius.
Now, if OB and OA be regarded as the positive direc
tions of the base and perpendicular, respectively,
and OB X and OA as their negative directions, the
sign of the hypotenuse being always positive, the
sign of any function may be determined by the signs
of the sides of the triangle upon which it depends. FlG g4
For example, the sine of the angle P"OB is -, and since a is positive the quantity has a positive
value; its cosine is -, and as b is measured in a negative direction from O the cosine must therefore be
negative.
In the first quadrant, between and 90, all quantities being positive, all functions will also be
positive.
In the second quadrant, between 90 and 180, sin A ( =- J is positive; cos A ( =- J has a nega
tive value because b is negative; tan A ( =r j is also negative because of 6. The cosecant, secant, and
cotangent have, as in all^ cases, the same signs as the sine, cosine, and tangent, respectively, being the
reciprocals of those quantities.
In the third quadrant, between 180 and 270, sin A ( =- J and cos A ( =- j are both negative,
because both a and 6 have negative values; tan A ( =rj is positive for the same reason.
In the fourth quadrant, between 270 and 360, sin A (=) is negative, cos A (=-) is positive,
and tan A ( =^ j is also negative.
From a consideration of the signs in the manner that has been indicated, the following relations
will appear:
sin A = sin (180 - A) = sin (180 + A) = - sin (360 A) = sin ( A),
cos A = cos (180 A) = cos (180 + A) = cos (360 A) = cos ( A),
tan A = tan (180 A) = tan (180 + A) = tan (360 A) = tan (A),
sin A = cos (90 A) = - cos (90 -f A) = - cos (270 A) = cos (270 + A).
Any similar relation may be deduced from the figure.
It is of great importance to have careful regard for the signs of the functions in all trigonometrical
solutions.
LOGARITHMS.
In order to abbreviate the tedious operations of multiplication and division with large numbers, a
series of numbers, called Logarithms, was invented by Lord Napier, by means of which the operation of
multiplication may be performed by addition, and that of division by subtraction. Numbers may be
involved to any power by simple multiplication and the root of any power extracted by simple division.
In Table 42 are given the logarithms of all numbers, from 1 to 9999; to each one "must be prefixed
an index, with a period or dot to separate it from the other part, as in decimal fractions; the logarithms
of the numbers from 1 to 100 are given in that table with their indices; but from 100 to 9999 the index
is left out for the sake of brevity; it may be supplied, however, by the general rule that the index of the
logarithm of any integer or mixed number is always one less than the number of integral places in the
natural number. Thus, the index of the logarithm of any number (integral or mixed) between 10 and
61828 16 18
272 RULES AND PRINCIPLES OF MATHEMATICS.
100 is 1; from 100 to 1000 it is 2 ; from 1000 to 10000 it is 3, etc.; the method of finding the logarithms
from this table will be evident from the rules that follow:
To find the logarithm of any number less than 100, enter the first page of the table, and opposite the
given number will be found the logarithm with its index prefixed. Thus, opposite 71 is 1.85126, which
is its logarithm.
To find the logarithm of any number between 100 and 1000, find the given number in the left-hand col
umn of the table of logarithms, and immediately under in the next column is a number, to which must
be prefixed the number 2 as an index (because the number consists of three places of figures), and the
required logarithm will be found. Thus, if the logarithm of 149 was required, this number being found
in the left hand column, against it, in the column marked at the top (or bottom) is found 17319, pre
fixing to which the index 2, we have the logarithm of 149 = 2.17319.
To find the logarithm of any number between 1000 and 10000, find the three left-hand figures of the given
number in the left-hand column of the table of logarithms, opposite to which, in the column that is
marked at the top (or bottom) with the fourth figure, is to be found the required logarithm, to which
must be prefixed the index 3, because the number contains 4 places of figures. Thus, if the logarithm
of 1495 was required, opposite to 149, and in the column marked 5 at the top (or bottom) is 17464, to
which prefix the index 3, and we have the logarithm, 3.17464.
To find the logarithm of any number above 10000, find the first three figures of the given number in the
left-hand column of the table, and the fourth figure at the top or bottom, and take out the corresponding
logarithm as in the preceding rule; take also the difference between this logarithm and the next greater,
and multiply it by the remaining figure or figures of the number whose logarithm is sought, pointing off
as many decimal places in the product as there are figures in the multiplier. To facilitate the calcula
tion of the proportional parts several small tables are placed in the margin, which give the correction
corresponding to the difference, and to the fifth figure of the proposed number. Thus, if the logarithm
of 14957 was required, opposite to 149, and under 5, is 17464; the difference between this and the next
greater number, 17493, is 29; this multiplied by 7 (the last figure of the givt:n number) gives 203;
pointing off the right-hand figure gives 20.3 (or 20) to be added to 17464, which makes 17484; to this,
prefixing the index 4, we have the logarithm sought, 4.17484. This correction, 20, may also be found
by inspection in the small table in the margin, marked at the top 29; opposite to the fifth figure of the
number, 7, in the left-hand column, is the corresponding correction, 20, in the right-hand column.
Again, if the logarithm of 1495738 was required, the logarithm corresponding to 149 at the left, and
5 at the top, is, as in the last example, 17464; the difference between this and the next greater is 29;
multiplying this by 738 (the given number excluding the first four figures) gives 21402; crossing off the
three right-hand figures of this product (because the number 738 consists of three figures) , we have the
correction 21 to be added to 17464; and the index to be prefixed is 6, because the given number consists
of 7 places of figures; therefore the required logarithm is 6.17485. This correction, 21, may be found as
above, by means of the marginal table marked at the top 29, taking at the side 7.38 (or 7 nearly), to
which corresponds 21, as before.
To find the logarithm of any mixed decimal number, find the logarithm of the number, as if it were
an integer, by the preceding rules, to which prefix the index of the integral part of the given number.
Thus, if the logarithm of the mixed decimal 149 5738 was required, find the logarithm of 1495738, with
out noticing the decimal point; this, in the last example, was found to be 17485; to this prefix the index
2, corresponding to the integral part 149; the logarithm sought will therefore be 2. 17485.
To find the logarithm of any decimal fraction less than unity, it must be observed that the index of the
logarithm of any number less than unity is negative; but, to avoid the mixture of positive and negative
quantities, it is common to borrow 10 in the index, which, in most cases, may afterwards be neglected
in summing them with other indices; thus, instead of writing the index ], it is written + 9; instead
of 2 we may write + 8; and so on. In this way we may find the logarithm of any decimal fraction
by the following rule: Find the logarithm of a fraction as if it were a whole number; see how many
ciphers precede the first figure of the decimal fraction, subtract that number from 9, and the remainder
will be the index of the given fraction. Thus the logarithm of 0.0391 is 8.59218 10; the logarithm of
0.25 is 9.39794 10; the logarithm of 0.0000025 is 4.39794 - 10, etc. In most cases the writing of 10
after the logarithm may be dispensed with, as it will be quite apparent whether the logarithm has a
positive or a negative index.
To find the number corresponding to any logarithm, seek in the column marked at top and bottom
the next smallest logarithm, neglecting the index; write down the number in the side column abreast
which this is found, and this will give the first three figures of the required number; follow the line
until the logarithm next smaller than the given one is found, and the fourth figure of the required
number will be at the top and bottom of the column in which this stands; take the difference between
this next smaller logarithm and the next larger one in the table, and also the difference between the
next smaller logarithm and the given one; entering the small marginal table which has for its heading
the first-named difference, and finding in the right-hand c lumn of that table the last-named difference,
there will appear abreast the latter, in the left-hand column, the fifth figure of the required number.
Where it is desired to determine figures beyond the fifth for the corresponding number, the difference
between the next lower logarithm and the given one may be divided by the difference between the
next lower and next higher ones, and the quotient (disregarding the decimal point, but retaining any
ciphers that may come between the decimal point and the significant figures) will be the fifth and suc
ceeding figures of the number sought. Having found the figures of the corresponding number, point
off from the left a number of figures which shall be one greater than the index number, and there place
a decimal point. In this operation of placing the decimal point, proper account must be taken of the
negative value of any index.
Thus, if the number corresponding to the logarithm 1.52634 were required, find 52634 in the column
marked at the top or bottom, and opposite to it is 336; now, the index being 1, the required number
must consist of two integral places; therefore it is 33.6.
If the number corresponding to the logarithm 2.57345 were required, look in the column and find
in it, against the number 374, the logarithm 57287, and, guiding the eye along that line, find the given
BULES AND PRINCIPLES OF MATHEMATICS.
273
logarithm, 57345, in the column marked 5; therefore th mixed number sought is 3745, and since the
index is 2, the integral part must consist of 3 places; therefore the number sought is 374.5. If the index
be 1 the number will be 37.45, and if the index be the number will be 3.745. If the index be 8,
corresponding to a number less than unity, the number will be 0.03745.
Again, if the number corresponding to the logarithm 3.57811 were required, find, against 378 and
under 5, the logarithm 57807, the difference between this and the next greater logarithm, 57818, being
11, and the difference between 57807 and the given logarithm, 57811, being 4; in the marginal table
headed 11, find in the right-hand column the number 4, and abreast the latter appears the figure 4,
which is the fifth figure of the required number; hence the figures are 37854; pointing off from the
left 3 -f 1 = 4 places, the number is 3785.4.
If the given logarithm were 5.57811, since the index 5 requires that there shall be six places in the
whole number, it is desirable to seek accuracy to the sixth figure. The logarithmic part being the
same as in the example immediately preceding, it is found as before that the first four figures are 3785,
the difference between the next lower and next greater logarithms is 11, and between the next lower
logarithm and the given one is 4; divide 4 by 11 and the quotient is .36; drop the decimal point, annex
and point off, and the number required is found to be 378536.
It may be remarked that in using five-place logarithm tables it is not generally to be expected that
results will be exact beyond the fifth figure.
To show, at one view, the indices corresponding to mixed and decimal numbers, the following
examples are given:
Mixed number. Logarithms.
40943.0.. Log. 4.61218
4094.3 Log. 3.61218
409.43 Log. 2.61218
40.943 Log. 1.61218
4.0943 Log. 0.61218
Decimal number. Logarithms.
0. 40943 Log. 9. 6121810
0.040943 Log. 8.61218-10
0.0040943 Log. 7. 61218-10
0.00040943 Log. 6.61218-10
0.000040943 Log. 5. 61218-10
To perform multiplication by logarithms, add the logarithms of the two numbers to be multiplied and
the sum will be the logarithm of their product.
EXAMPLE I.
Multiply 25 by 35.
25.. ..Log. 1.39794
35 Log. 1.54407
Product, 875 Log. 2.94201
EXAMPLE II.
Multiply 22.4 by 1.8.
22.4 Log. 1.35025
1.8 Log. 0.25527
Product, 40.32.. ..Log. 1.60552
EXAMPLE III.
Multiply 3.26 by 0.0025.
3.26 Log. 0.51322
0.0025 Log. 7.39794
Product, 0. 00815 Log. 7.91116
EXAMPLE IV.
Multiply 0.25 by 0.003.
0.25 Log. 9.39794
0.003 Log. 7.47712
Product, 0.00075 Log. 6.87506
In the last example, the sum of the two logarithms is really 16.8750620; this is the same as
6.8750610, or, remembering that the quantity is less than unity, simply 6.87506.
To perform division by logarithms, from the logarithm of the dividend subtract the logarithm of the
divisor; the remainder will be the logarithm of the quotient.
EXAMPLE I.
Divide 875 by 25.
875.. ..Log. 2.94201
25 Log. 1.39794
Quotient, 35 Log. 1.54407
EXAMPLE II.
Divide 40.32 by 22.4.
40.32.... ..Log. 1.60552
22.4 Log. 1.35025
Quotient, 1.8 Log. 0.25527
EXAMPLE III.
Divide 0.00815 by 0.0025.
0.00815 .. ..Log. 7.91116
0.0025 Log. 7.39794
Quotient, 3. 26 Log. 0.51322
EXAMPLE IV.
Divide 0.00075 by 0.025.
0.00075 .. ..Log. 6.87506
0.025 Log. 8.39794
Quotient, 0. 03 Log. 8. 47712
In Example III both the divisor and dividend are fractions less than unity, and the divisor is the
lesser; consequently the quotient is greater than unity. In Example IV both fractions are less than
unity; and, since the divisor is the greater, its logarithm is greater than that of the dividend; for this
reason it is necessary to borrow 10 in the index before making the subtraction, that is, to regard the
logarithm of .00075 as 16.87506 20; hence the quotient is less than unity.
274
KULES AND PRINCIPLES OF MATHEMATICS.
The arithmetical complement of the logarithm of a number, usually called the cologarithm of the
number, and denoted by colog, is the remainder obtained by subtracting the logarithm of the number
from the logarithm of unity. It is therefore the logarithm of the reciprocal of the number; and, since the
effect of dividing by any number is the same as that of multiplying by its reciprocal, it follows that, in
performing division by logarithms, we may either subtract the logarithm of the divisor or add the arith
metical complement of that logarithm. As the addition of a number of quantities can be performed
in a single operation, while in subtraction the difference between only two quantities can be taken at a
time, it is frequently a convenience to deal with the arithmetical complements rather than with the
logarithms themselves.
EXAMPLE III.
40.32X.00815
Simplify the expression, 22 .4 X .0025
40.32 Log. 1.60552
.00815 Log. 7.91116
22.4 Log. 1.35025 Colog. 8.64975
.0025 Log. 7.39794.. ..Colog. 2.60206
Result, 5.868 __ Log. 0.76849
EXAMPLE I.
Divide 875 by 25.
875 Log. 2.94201
25 Log. 1.39794 Colog. 8.60206
Quotient, 35 Log. 1.54407
EXAMPLE II.
Divide 0.00075 by 0.025.
0.00075 Log. 6.87506
0.026 Log. 8.39794 Colog. 1.60206
Quotient, 0.03 Log. 8.47712
To perform involution by logarithms, multiply the logarithm of the given number by the index of the
power to which the quantity is to be raised; the product will be the logarithm of the power sought.
EXAMPLE I.
Required the square of 18.
18 Log. 1.25527
2
Answer, 324 Log. 2.51054
EXAMPLE II.
Required the square of 6.4.
6.4.. ..Log. 0.80618
2
Answer, 40.96 Log. 1.61236
EXAMPLE III.
Required the cube of 13.
13 Log. 1.11394
3
Answer, 2197 Log. 3. 34182
EXAMPLE IV.
Required the cube of 0.25.
0.25 Log. 9.39794
3
Answer, 0.015625 Log. 8.19382
In the last example, the full product of the multiplication of 9.3979410 by 3 is 28.1938230, which
is equivalent to 8.1938210.
To perform evolution by logarithms divide the logarithm of the number by the index of the power;
the quotient will be the logarithm of the root sought. If the number whose root is to be extracted is a
decimal fraction lees than unity, increase the index of its logarithm by adding a number of tens which
shall be less by one than the index of the power before making the division.
EXAMPLE I.
Required the square root of 324.
324 Log. 2)2.51055
Answer. 18. ._ Log. 1.25527
EXAMPLE II.
Required the cube root of 2197.
2197 Log. 3)3.34183
Answer, 13 Log. 1.11394
EXAMPLE III.
Required the square root of 40.96.
40.96 Log. 2)1.61236
Answer, 6.4 Log. 0.80618
EXAMPLE IV.
Required the cube root of 0.015625.
0.015625 Log. 8.19382
Add 20 to the index 3)28.19382
Answer, 0.25 Log. 9.39794
In the last example the logarithm 8.19382 10 was converted into its equivalent form of 28.1938230,
which, divided by 3, gives 9.3979410.
To find the logarithm of any function of an angle, Table 44 must be employed. This table is so
arranged that on every page there appear the logarithms of all the functions of a certain angle A,
RULES AND PKINCIPLES OF MATHEMATICS. 275
together with those of the angles 90 A, 90-{-A, and 180 A; thus on each page may be found the
logarithms of the functions of four different angles. The number of degrees in the respective angles
are printed in bold-faced type, one in each corner of the page; the number of minutes corresponding
appear in one column at the left of the page and in anothei at the right; the names of the functions
to which the various logarithms correspond are printed at the top and bottom of the columns. The
invariable rule must be to take the name of the function froffrlhe top~~6r "the bottom of the page,
according as the number of degrees of the given angle is found at the top or bottom; and to take the
minutes from the right or left hand column, according as the number ot degrees is found at the right
or left hand side of the page; or, more briefly, take names of functions and number of minutes,
respectively, from the line and column nearest in position to the number of degrees.
Taking, as an example, the thirty-first page of the table, it will be found that 30 appears at the
upper left-hand corner, 149 at the upper right-hand, 59 at the lower right-hand, and 120 at the lower
left-hand corner. Suppose that it is desired to find the log. sine of 30 10 ; following the rule given, we
find KX in the left-hand column and Sine at the top ot the page, and abreast one and below the other is
the required logarithm, 9.70115. But if the log. sine of 59 10 were sought, as 59 appears below and at
the right of the page, the logarithm 9.93382 would be taken from the column marked Sine at the bottom
and abreast 10 / on the right. It may also be seen that log. sin 30 10 / =log. cos 59 5(K=log. cos
120 10 / =log. sin 149 50 / =9.70115, the equality of the functions agreeing with trigonometrical
deductions; (in this statement numerical values only are regarded, and not signs; the latter must, of
course, be taken into account in all operations) .
EXAMPLE I.
Required the log. sine, cosecant, tangent, cotan
gent, secant, and cosine of 28 37 .
Log. sin 9. 68029 Log. cot 10. 26313
Log. cosec 10. 31971 Log. sec 10. 05658
Log. tan 9. 73687 Log. cos 9. 94342
EXAMPLE II.
Required the log. sine, cosecant, tangent, cotan
gent, secant, and cosine of 75 42 .
Log. sin 9. 98633 Log. cot 9. 40636
Log. cosec 10. 01367 Log. sec 10. 60730
Log. tan 10. 59364 Log. cos 9. 39270
When the angle of which the logarithmic function is required is given to seconds, it becomes
necessary to interpolate between the logarithms given for the even minutes next below and next above;
this may be done either by computation or (except in a few cases) by inspection of the table.
To interpolate by computation, let n represent the number of seconds, D the difference between the
logarithms of the next lesser and next greater even minute, and d the difference between the logarithm
of the next lesser even minute and that of the required angle. Then,
It should be noted when the number of seconds is 30, 20, 15, or some similar number, permitting
the reduction of the fraction JL to a simple value, such as , , J, as the interpolation by this method
may thus be made with greater facility.
Haying obtained the difference of the logarithm from that of the next lower even minute, it must
be applied in the proper direction that is, if the function is such that its logarithm increases as the
angle increases, the logarithmic difference must be added; but if it decreases, then that difference must
be subtracted.
For example, let it be required to find the log. sin and log. cosec of 30 10 7 19". The log. sin of
30 10 7 is 9.70115; the difference between this logarithm and that of the sine of 30 IV (9.70137) is + 22,
which is D. Hence,
and the required logarithm is 9.70122. The log. cosec of 30 10 7 is 10.29885; the difference, D, between
that and log. cosec 30 IV (10.29863) is 22. In this case
therefore, log. cosec 30 10 7 19"= 10. 29878.
The method of interpolating by inspection consists in entering that column marked " Diff." which
is adjacent to the one from which the logarithmic function for the next lower minute is taken, and
finding, abreast the number in the left-hand minute column which corresponds to the seconds, the
required logarithmic difference; and the latter is to be added or subtracted according as the logarithms
increase or decrease with an increased angle. Thus, if it be required to find log. sin 30 10 7 19", find as
before log. sin 30 10 / =9. 70115, then, in the adjacent column headed "Diff." and abreast the number
of seconds, 19, in the left-hand minute column will be found 7, the logarithmic difference; fedd this, as
the function is increasing, and we have the required logarithm 9.70122. If log. cosec 30 l(Y 19 // be
sought, find log. cosec 30 6 10 / = 10. 29885; then in the adjacent difference column, which is the same as
was used for the sines, find as before the logarithmic difference, 7; and since this function decreases as
the angle increases, this must be subtracted; therefore, log. cosec 30 10 19"= 10. 29878.
This method of interpolation by inspection is not available in that portion of the table where the
logarithmic differences vary so rapidly that no values will apply alike to all the angles on the same
page; on such pages the difference for one minute is given in a column headed "Diff. 1 ," instead of
the usual difference for each second; in this case the interpolation must be made by^computation, the
given difference for one minute being D. In other parts of the table the interpolation by inspection
may be liable to slight error because of the variation in logarithmic difference for different angles on
the* same page; but the tabulated values are sufiiciently accurate for the usual calculations in navigation.
276
RULES AND PRINCIPLES OF MATHEMATICS.
It will be evident that while the methods explained have contemplated entering the tables with a
smaller angle and interpolating ahead, it would be equally correct to enter with a greater angle and
nterpolate back for the proper number of minutes, making the requisite change in the sign of the
icorrection.
EXAMPLE I. EXAMPLE II.
Required the log. sine, cosine, and tangent of
42 57 06".
Log. sin
Log. cos
Log. tan
For 42 57
d
For 42 67 06"
9. 83338
9. 86448
9. 96890
+1
1
+3
9. 83339
9. 86447
9. 96893
Required the log.
of 175 32 36".
secant, cosecant, and cotangent
Log. sec
Log. cosec
Log. cot
For 175 32
d
For 175 32 36"
10. 00132
11. 10858
11. 10726
I
+97
+98
10. 00131
11. 10955
11. 10824
It should be observed that, for uniformity and convenience, all logarithms given in Table 44 have
been increased by 10 in the index, and it is understood that 10 ought properly to be written after
each; thus all logarithms under 10.00000 represent functions whose value is less than unity, and all
over 10.00000 those greater than unity; for example, 11.10726 is the logarithm of a number in which
the decimal point should be placed after the second figure from the left.
To find the angle corresponding to any logarithmic function, the process is the reverse of the one just
described. Find, in the column marked with the name of the function, either at top or bottom, the
two logarithms between which the given one falls; write down the degrees and minutes of the lesser of
the two corresponding angles, which will be the degrees and minutes of the angle required. Call the
difference between the two tabulated logarithms D, and the difference between the given logarithm and
that which corresponds to the lesser angle, d; then if n represents the number of seconds, we have:
Or, the same may be obtained by inspection (except where, as before explained, the differences
for seconds are not tabulated ) by finding, in the Diff . column adjacent to that from which the logarithm
was taken, the logarithmic difference, d, and noting the number of seconds abreast which it stands in
the left-hand minute column.
Interpolation may be also made in the reverse direction from the next greater even minute.
Thus, if it be required to find the angle corresponding to log. sin 9.61400, we find log. sin 24 16 ,
9.61382, and log. sin 24 17 , 9.61411; hence D=29, and d=18;
n=4X 60=37;
and the angle is 24 16 37". Or, in adjacent column headed "Diff.," 18 would be found abreast 38,
39, or 40 (seconds) in the left-hand minute column a correspondence sufficiently close for navigation
work.
If the angle were known to be in the second quadrant, we find log. sin 155 43 , 9.61411, and log.
sin 155 44 , 9.61382; here D=29, and d=ll;
therefore, the angle is 155 43 23". Or, in adjacent "Diff." column find, abreast 11, 23 or 24 seconds.
EXAMPLE I. EXAMPLE II.
Find angles less than 90 corresponding to log.
cot 10.33621, log. sec 10.11579, and log. cos 8. 70542.
Log. cot 10.33621
Log. sec 10.11579
Log. cos 8. 70542
u
24 45
8
15
40 00
4
22
87 05
116
28
Find angles in second quadrant corresponding to
log. tan 10.15593, log. sin 8.87926, and log. cosec
10.04944.
Log.
Log.
Log.
tan
sin
cosec
10. 15593
8. 87926
10. 04944
o
r
d
//
124
175
116
55
39
49
19
69
3
42
25
27
given
The Hour Columns in Table 44 give the measure in time corresponding to twice the angular distance
a in arc. Thus, abreast the angle 13 00 stands in the P. M. column l h 44 m 00 s , corresponding in
time to 2X13 00 ; and in the A. M. column 10 h 16 m 00 s , which is the same subtracted from 12 h . These
columns are of use in working the various formulae which involve functions of half the hour angle.
Interpolation for values intermediate to those given in the tables is made on the same principle as for
the angular measure; this operation may be performed by inspection by the use of the small tables at
the bottom of each page, where n, the number of seconds of time, is given in bold-faced type, and d, the
logarithmic difference for the respective columns, appears below.
EXAMPLE I.
Given t=l h 48 m 44", find log. cot J t.
log. cot. i t
For l h 48 m 40 ,
Diff. for 4% Col. B
For l h 48 m 44 ,
10. 61687
28
EXAMPLE II.
Given log. sin J t, 9.91394, find the Hour A. M.
corresponding.
For 9. 91389, 4 h 39 m 12
Diff. for 5, Col. C 5
log. cot i t 10. 61659
For 9.91394,
4 39 07
RULES AND PRINCIPLES OF MATHEMATICS. 277
MISCELLANEOUS USEFUL DATA.
Earth s Polar radius=6,356,5S3.8 meters.
Earth s Equatorial radius=6,378,206.4 meters.
Earth s Compression=oqo A^
Earth s Eccentricity =0.0822719 log 8. 9152513.
Number of feet in o ne statute mile=5280 log 3. 7226339.
Number of feet in one nautical mile=6080.27 log 3. 7839229.
Sine of 1"= 0.00000485 log 4. 6855749.
Sine of 1 / =0.0002U089 log 6. 4637261.
The Napierian base =2.7182818 log 0. 4342945.
The modulus of common logarithms =0.4342945 log 9. 6377843.
French meter in English feet, 3.2808333 log 0. 5159842.
French meter in English statute miles, 0.000621370 log 6. 7933503.
French meter in nautical miles, 0.000539568 log 6. 7320613.
1 pound Avoirdupois =7, 000 grains Troy.
French gramme=0. 00220606 Imperial pound Troy.
French kilogram me=0. 0196969 English cwts.
Cubic inch of distilled water, in grains=252.458. ]
Cubic foot of water, in ounces Troy =908. 8488.
Cubic foot of water, in pounds Troy=75.7374. \ Bar. 30.00 in.; ther. 62 F
Cubic foot of water, in ounces Avoirdupois=997.1369691.
Cubic foot of water, in pounds A voirdupois=62. 3210606. J
Length of pendulum which vibrates second at Greenwich, 39.1393 inches.
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
The following table contains the latitude and longitude of a large number of places, together with
lunitidal intervals and tidal ranges at the more important ones. It is arranged geographically and followed
by an alphabetical index.
The geographical position generally relates to some specified exact location, and is based upon the
best available authority. The tidal data relate to the waters adjacent to the point whose latitude and
longitude are given, being abstracted from the Tide Tables published by the United States Coast and
Geodetic Survey.
The high-water and low- water lunitidal intervals represent the mean intervals between the moon s
transit and the time of next succeeding high and low waters throughout a lunar month. The spring
and neap ranges are the differences in height between high water and low water at spring and at neap
tides. For those places where the tide is chiefly of a diurnal type, and where there is usually but one
high and one low water during a lunar day, the tidal values are bracketed; in such cases the lunitidal
intervals are for the semidiurnal part of the tide (which, however, is only appreciable for a few days
when the moon is near the equator), and the range given in the column headed "Spg." does not, as in
other cases, apply to the spring tide, but to the greatest periodic daily range, which usually occurs a day
or two after the moon attains its extreme of declination, and is therefore near one of the tropics. As those
places where the diurnal type predominates seldom experience large tidal effects, the general data
furnished regarding such tides will suffice for the ordinary purpose of the navigator. The method of
finding the time of high or low water from this table is illustrated in article 504, Chapter XX.
278
APPENDIX IV. [Page 279
MARITIME POSITIONS AND TIDAL DATA.
EAST COAST OF NORTH AMERICA.
P
Place.
Lat. N.
Long.W.
Lon.Int.
Range.
H. W.
L.W.
Spg. Xeap.
Labrador.
Salisbury Island: E. pt
ft. m.
ft. m.
A
ft.
63 27 00
63 06 00
62 37 00
62 35 00
62 48 00
62 50 00
62 30 00
62 07 00
61 18 00
60 10 00
60 40 00
60 52 00
60 33 00
61 21 00
61 40 00
60 00 00
59 48 00
59 07 00
57 35 00
57 00 00
56 32 45
55 27 04
55 13 33
54 55 50
54 26 55
54 00 05
53 50 00
53 42 37
53 34 25
53 26 00
52 40 07
52 21 16
52 15 36
52 06 00
51 53 00
51 38 48
50 42 10
49 59 54
49 53 00
49 45 29
49 35 40
49 41 20
49 36 50
49 15 20
49 04 20
48 42 01
48 30 15
48 16 55
47 53 10
48 08 58
47 42 45
47 48 30
47 34 02
46 39 24
46 37 04
46 43 20
46 49 34
47 17 55
47 00 26
46 56 30
76 30 00
77 50 00
78 08 00
77 33 00
74 00 00
75 20 00
74 03 00
72 25 00
70 02 00
67 05 00
67 50 00
64 40 00
64 12 00
65 00 00
64 30 00
64 28 00
64 07 15
63 20 00
61 20 00
62 07 00
61 40 13
60 12 34
59 OS 01
57 56 40
57 12 40
56 31 31
56 23 00
56 59 50
55 58 39
55 35 48
55 44 29
55 38 03
55 32 20
55 41 00
55 22 10
55 25 12
55 35 30
55 21 33
55 37 17
53 10 56
53 45 00
54 47 35
54 12 00
53 25 12
53 37 45
53 04 42
53 02 40
53 23 35
53 23 20
52 47 42
53 08 11
52 47 20
52 40 54
53 04 30
53 31 55
53 22 10
54 11 42
53 58 43
55 08 49
55 32 00
XnTtino harn Tslp.nd S pt
8 58
2 46
13.5
6.1
Digges Island: W extreme
Cape Wostenholme
Charles Island* E pt
W pt
Cape Weggs
Prince of Wales Sound: Center of ent
Cape of Hopes Advance
Akpatok Island* E pt
Green Island: XE. pt
Button Islands* N pt ...
Cape Chiolleio-h
Resolution Island: S. pt., Hutton h dl d. .
E. pt., C. Resolution. .
Black Head
Eclipse Harbor* E side
8 00
7 00
1 48
48
5.0
5.2
2.0
2.1
Xachvack Bav: Islands off entrance
Saddle Island . .
Port Manvers: Entrance.
Xain: Church
7 00
5 30
48
11 43
6.5
6.9
3.0
3.2
Hopedale Harbor: Hill to E d
Aillick Harbor* Cape Mokkivik
Cape Harrison* N extreme
Indian Harbor: Obsy
6 10
12 23
7.0
3.2
Outer Gannet Island: Summit
Greadv Harbor
Cartwfieht Harbor: Caribou Castle
Indian Tickle* Summit
6 27
15
6.0
2.8
Roundhill Island* Summit
Occasional Harbor: E. summit of Twin I.
Cape St Lewis: SE pt . . . .
6 38
6 30
26
18
5.0
3.5
2.3
1.6
Battle Islands: XE extreme SE I
Table Head
Belle Isle* Lighthouse
Newfoundland.
Cape Bauld: Lighthouse
Bell Island: S end... .
Cape St John* Gull Inland light
Tilt Cove, Union Copper
Mine
Funk Island" Summit
Offer Wadham: Lighthouse
Toulinguet Inlands* Li ty hthoii <s e
Seldom-come-bv Harbor* Ship Hill
Cape Freeh- Gull I
Greenspond Inland
Cape Bona vista* Lighthouse
Cat ilina Harbor* Green I li^hthou^
Bonaventu^e Head
Hearts Content* Lighthouse
7 23
1 11
4.1
1.9
Baccalieu Island* Lighthouse
Harbor Grace* Lighthouse on beach
7 15
1 03
3.3
1.5
Cape St Francis* Li^hthou^e
St. Johns Harbor: Chain Rock Battery. . .
Cape Race: Lighthouse
Cape Pine* Li^hthou^
7 12
6 50
1 01
38
3.3
6.5
1.5
3.0
Trepassev Harbor* Shingle Xeck
6 50
8 20
38
2 08
6.6
7.2
3.1
3.3
Cape St Marv: Lighthouse
Little Placentia Harbor: W. side Coopers
Cove
Burin I c land* Li fr hthou <; e
! Launt Gr. Laun R. C Church..
8 05
1 53
7.0
3.2
Page 280] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
EAST COAST OF NORTH AMERICA Continued.
o
Place.
Lat. N.
Long. W.
Lun. Int.
Range.
H. W.
L.W.
Spg.
Neap.
Labrador. Newfoundland.
St. Pierre: U. S. Coast Survey Station
Brunet Island: Mercers Bd. lighthouse. . .
Boar Islands: Burgoo I light-house
h. m.
8 23
8 53
8 22
8 50
h. m.
2 11
2 41
2 10
2 38
A.
6.6
6.5
6.2
6.0
ft.
3.1
3.0
2.9
2.8
46 46 51
47 15 30
47 35 13
47 39 50
47 37 00
47 52 30
48 33 48
49 55 20
50 38 30
50 41 50
51 02 00
51 17 25
51 24 10
51 38 00
51 58 00
51 27 35
51 22 45
51 22 26
51 27 22
51 21 40
50 47 30
50 46 44
50 31 10
50 14 00
50 09 30
50 11 00
50 06 00
50 12 27
50 05 40
49 19 35
46 48 23
46 47 59
45 29 57
45 23 30
48 31 25
49 06 00
49 15 40
48 51 37
48 45 15
49 05 20
49 23 45
48 29 30
48 24 00
48 12 00
48 01 00
48 04 24
48 01 07
47 14 00
47 05 00
47 03 46
46 33 56
46 27 15
46 11 36
47 50 40
47 37 40
47 16 30
47 14 23
47 16 03
56 10 36
55 51 40
57 36 52
58 24 10
59 18 00
59 23 40
59 13 10
57 50 00
57 17 07
57 25 00
57 03 50
56 44 45
56 33 40
55 53 52
55 50 20
56 51 05
57 08 00
57 10 04
57 13 21
57 46 00
58 51 30
58 59 20
59 20 25
59 45 00
59 57 00
60 08 00
61 44 00
63 27 03
66 22 44
67 21 55
71 12 19
71 13 10
73 34 08
75 42 59
68 27 40
66 46 00
65 19 30
64 12 00
64 09 35
61 42 30
63 35 46
64 08 00
64 18 00
64 46 30
65 19 00
66 22 10
64 29 20
65 02 00
64 47 33
63 58 49
63 41 35
61 57 35
63 06 58
61 08 32
61 24 30
61 41 20
61 49 38
62 12 25
La Poile Bay: Gr. Espic Church..
Cape Ray: Lighthouse
Codroy Island: S. side Boat Harbor
8 50
2 32
4.3
2.1
Cape St. George: Red L, SE. pt
Cow Head: N W. extreme
9 40
3 13
4.9
2.5
PortSaunders: Two Hills Pt
Rich Point: Lighthouse
F6rolle Pena: New Ferolle Pt.
Flower Cove: Capstan Pt
Green Island: 150 fms. from NE. end
Cape Norman* Lighthouse
Chateau Bay S pt Castle I
Amour Point: Li<*hthouse
Wood Island: S pt
Greenly Island: Lighthouse
Bradore Bay: Obs. Spot, Jones Pt
Old Fort Island: Center..
Great Mekattina Island: SE.pt
Mokattina Harbor: S. point of Dead Cove.
Little Mekattina L: S. pt. C. McKinnon.
St Mary Reefs
South Makers Ledge
Cape Whittle
R. and G. of St. Lawrence.
Natashquan Point: S ed< T e
1 25
6 45
4.0
2.0
C learwater Point: SW extreme
CUOUSB! Island: Lighthouse
1 43
1 48
6 07
7 05
7 18
54
8.1
10.8
14.6
6.0
8.0
10.8
Point do Monts: Lighthouse
Quebec: Mann s Bastion, Citadel
Qiiobno: Bomier s Hill Obsy
Montreal: St. James Cathedral
Ottawa: Dominion Observatory
Father Point: Lighthouse.
1 52
1 46
1 33
1 25
7 33
7 13
6 50
6 40
12.0
10.5
6.4
5.5
8.9
7.8
4.7
4.1
Cape Chatto: Extreme
Cape Magdalen : Lighthouse
(, npo Rosier: Lighthouse
Cape Ga^p6: Lighthouse
Anticosti Island: Heath Pt. lighthouse. . .
SW. pt. lighthouse
Bonaventuro Island: E. pt
1 20
1 25
6 35
6 40
3.6
4.9
1.8
2.5
*
I
I.eander Shoal
Macquereau Point
1 55
2 20
3 10
2 00
4 16
7 33
8 07
9 10
8 25
10 59
4.7
4.8
8.1
4.0
2.3
2.3
2.4
4.1
2.0
1.2
Chaleur Bay: Carlisle
Dalhousie I
Miscou Island: Birch Pt. lighthouse
Miramichi Bay: Portage I., N. pt.
Point Earn men SIP: Lignthoiiso
North Point: Lighthouse .
4 20
5 15
8 17
11 07
11 00
11 55
2 20
4 23
2.4
1.8
1.4
6.4
1.2
0.9
0.7
3.2
l M
h
*t
Malpeque Bay: Rovalty Pt .
East Point: Lighthouse
Charlottetown: Blackhouse Pt. light
Gt Bird Rock* Lighthouse
l
East Island * E extreme
Entry Island: Lighthouse..
Amherst Hbr : N. side of entrance
Deadrnan Rock: W. pt
APPENDIX IV. [Page 281
MARITIME POSITIONS AND TIDAL DATA.
EAST COAST OF NORTH AMERICA Continued.
I
Place.
Lat. X.
Long. W.
Lun. Int.
Range.
H.W.
L.W.
Spg.
Neap.
St. Paul Island: Lighthouse, NE. end
Lighthouse, SW. end
Cape North: Lighthouse
h. m.
8 30
A. m.
2 12
7
ft.
1.4
47 13 50
47 11 20
47 01 45
46 21 00
46 12 25
46 02 15
45 54 34
45 28 00
46 00 00
43 58 14
45 40 50
45 52 00
45 41 42
45 30 48
45 19 49
45 11 58
45 06 15
45 00 35
44 39 38
44 26 10
44 34 00
44 29 00
44 21 45
44 12 00
44 02 00
43 48 30
43 37 15
43 23 19
43 23 34
43 47 28
44 05 20
44 14 57
44 41 34
45 14 55
45 19 00
45 18 40
45 35 34
45 19 30
45 14 20
45 03 40
45 04 00
45 04 06
44 57 40
44 45 52
44 30 38
44 30 07
45 11 05
44 54 15
44 48 55
44 43 01
44 22 03
44 14 29
43 58 08
44 48 23
44 25 29
44 06 06
43 47 03
43 45 53
43 42 26
60 08 32
60 09 50
60 23 27
60 27 00
60 12 50
59 40 25
59 59 26
61 03 00
61 36 00
59 44 15
62 42 10
61 52 00
61 29 10
61 01 47
60 55 41
61 08 14
61 32 40
61 52 45
63 35 22
63 33 30
63 54 00
64 06 00
64 17 35
64 18 00
64 37 30
64 47 15
65 15 45
65 37 11
66 00 52
66 09 21
66 12 40
66 23 38
65 47 20
65 00 45
64 57 00
63 48 30
64 46 55
65 32 00
66 03 20
66 27 40
66 49 00
67 02 52
66 54 10
66 44 00
66 47 00
67 06 13
67 16 50
66 59 14
66 57 04
67 27 22
67 51 51
68 11 58
68 07 44
68 46 59
69 00 19
69 06 52
68 51 28
69 18 59
69 45 32
8 35
8 25
8 10
2 17
2 13
2 05
3.1
6.0
5.0
1.6
3.7
3.1
M
c
ti
St. Anns Harbor: E. pt. entrance
Sydney Harbor: Lighthouse
Scatari Island: Lighthouse, NE. pt ..
Louisburg: Lighthouse, NE. pt
7 45
7 55
9 05
1 35
1 47
2 47
5.0
5.0
3.5
3.1
3.1
1.8
Madame Island * S pt
Port Hood Just-au-corps I
Sable Island: Lighthouse, E end
Pictou: Customhouse
9 34
9 20
9 26
7 55
7 43
7 45
3 13
3 00
3 10
1 47
1 36
1 38
3.9
2.8
3.1
5.0
6.5
6.6
2.0
1.4
1.6
3.1
4.0
4.1
Nova Scotia.
Cape St. George
North Canso: Lighthouse, NW. entrance.
Arichat Harbor: R. C. Church steeple
Cape Canso: Cranberry I., lighthouse
White Head Island: Lighthouse .
Green Island: Lighthouse....
Wedge Island : Lighthouse . . .
Halifax: Dockyard observatory..
7 34
146
5.2
3.2
Sambro Island* Lighthouse
Margaret Bay: Shut-in I
7 32
1 30
7.1
4.4
Tancook Island
Lunenburg: Battery Pt light
7 39
1 36
7.0
4.3
Cape La Have: Black Rock.
Coffin Island" Lighthouse
Little Hope Island* Lighthouse
Shelburne Hbr. : Two lights, McNutts 1 . .
Cape Sable: Lighthouse
8 17
9 35
10 00
2 05
3 23
3 41
8.5
12.8
16.0
5.2
9.5
11.8
Seal Island: Lighthouse
Yarmouth : Cape Fourchu light
Cape St. Mary
Bryer Island : Lighthouse
10 29
10 49
11 07
4 36
4 41
5 27
20.8
27.5
33.0
15.4
20.4
24.4
Annapolis Harbor: Prim Pt. light.
Haute Island: Lighthouse
Cape Chignecto ..
Rurntcnat TTpad: Lighthouse ,
27
7 27
50.5
37.4
Cape Enrag: Lighthouse
tf
^
/
9
a
2
c
"3
Cape Quaco : Lighthouse ....
11 21
11 07
11 04
11 09
11 00
5 56
4 58
5 26
5 08
5 00
30.0
23.9
24.5
23.3
24.9
22.2
17.7
18.2
17.1
18.2
St. Johns: Partridge I. light. . .
Cape Lepreau : Lighthouse
L Etang Harbor: S. pt. tower
St. Andrew: S pt. li<>ut
Campo Bello Island: Lighthouse, N. pt. .
Grand Manan Island : Lighthouse, NE.pt.
Gannet Rock* Lighthouse NE pt
11 02
5 21
22.5
16.7
Machias Island* Lighthouse
10 51
11 36
11 09
4 56
5 40
5 05
18.0
23.3
20.9
13.2
17.1
15.2
Calais: Astronomical station
Eastport: Cong. Church..
Quoddy Head* Lighthouse
Machias- Town Hall
11 02
4 59
15.5
11.3
Petit Manan Island : Lighthouse
Bakers Island: Lighthouse
Mount Desert Rock* Lighthouse
Bangor* Thomas Hill
23
11 35
11 09
10 45
6 47
5 22
4 55
4 31
15.1
11.7
11.0
10.2
11.0
8.6
8.1
7.5
Belfast: Methodist Church
Rockland : Episcopal Church
Matinicus Rock : Lighthouse
Monhegan Island * Lighthouse
Seguin Island * Lighthouse
Page 282] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
EAST COAST OP NORTH AMERICA Continued.
1
6
Place.
Lat. N.
Long. W.
Lun. Int.
Range.
H.W.
L.w.
Spg.
Neap.
Maine.
Bath: Winter St. Church
ft. TO.
12 13
ft. m.
6 16
ft.
7.9
ft.
5.8
43 54 55
43 54 29
44 18 52
43 39 28
43 37 23
43 33 51
43 27 24
43 07 17
43 03 32
43 04 56
43 04 16
42 56 15
42 58 02
42 48 30
42 48 55
42 41 07
42 39 43
42 38 21
42 36 46
42 36 07
42 32 48
42 31 00
42 30 20
42 22 48
42 22 22
42 21 28
42 19 41
42 16 11
41 58 44
42 00 12
41 43 20
42 02 23
41 40 17
41 33 34
41 16 55
40 37 05
41 17 01
41 28 08
41 28 51
41 20 55
41 24 52
41 38 10
41 26 30
41 26 58
41 29 07
41 38 34
41 50 21
41 21 40
41 09 10
41 18 14
41 04 16
41 19 31
41 21 16
41 12 23
41 08 29
41 10 25
41 16 17
41 19 22
69 49 00
69 57 44
69 46 37
70 15 18
70 12 30
70 12 11
70 19 46
70 28 37
70 41 49
70 44 22
70 42 34
70 50 12
70 37 25
70 52 28
70 49 10
70 46 00
70 40 55
70 34 31
70 39 59
70 39 58
70 51 23
70 53 03
70 50 03
71 07 46
71 03 05
71 03 50
70 53 26
70 45 35
70 39 12
70 36 04
70 16 52
70 03 40
69 57 01
69 59 39
70 05 57
69 36 33
69 57 57
70 45 29
70 36 01
70 50 08
70 57 01
70 55 36
71 13 30
71 24 00
71 19 40
71 15 39
71 23 59
71 28 55
71 33 08
71 51 32
71 51 27
71 54 49
72 04 47
72 06 26
72 08 44
72 12 43
72 20 37
72 55 09
Brunswick* College spire
Augusta: Baptist Church
2 54
11 06
10 18
4 51
4.9
10.1
3.6
7.3
Portland : Customhouse ....
Portland. Head lighthouse
Cape Elizabeth* Lighthouse (west)
Wood Island* Lighthouse
11 12
4 51
10.2
7.5
Boon Island Lighthouse
WTiale Back: Lighthouse
5
K
Portsmouth: Navy-yard flagstaff
11 23
5 09
10.5
7.7
Fort Constitution
Hampton* Baptist Church
Isles of Shoals* White I lighthouse
11 19
11 23
4 58
5 10
10.0
9.1
7.3
6.6
Newburyport : Academy
Massachusetts.
Plum I. lighthouse
Ipswich: Lighthouse (rear)
11 17
11 13
5 04
5 00
10.1
10.1
7.4
7.4
Annisquam Harbor: Lighthouse
Cape Ann: Thatchers I. lighthouse (N.). .
Gloucester" Universalist Church
Ten-pound I lighthouse
11 02
4 49
10.2
7.5
Beverly: Hospital Pt lighthouse
Salem: Derby 8 Wharf lighthouse
11 16
11 09
5 03
4 57
10.6
10.6
7.7
7.7
Marblehead: Lighthouse
Cambridge: Harvard Observatory
Boston: Navy-yard flagstaff
11 27
5 17
11.0
8.1
Pt.at.ft "HVmfifi
Little Brewster I. lighthouse
Minots Ledge: Lighthouse
11 09
4 56
10.9
8.0
Plymouth: Pierhead.
Gurnet lighthouse
11 23
11 36
5 11
5 25
10.8
11.6
7.9
8.5
Barnstable: Lighthouse
Cape Cod: Highland slight house
Chatham: Lighthouse (south)
12 11
12 00
04
5 57
5 48
6 00
4.6
4.3
3.8
3.4
3.1
2.3
Monomoy Point : Lighthouse
Nantucket: South Church
Nantucket Shoals: Lightship
Sankaty Hpad " Lightboiipp
Tarpaulin Cove: Lighthouse
7 51
11 34
7 31
7 36
7 57
7 40
7 40
7 48
7 53
8 12
7 32
7 33
8 49
8 20
9 09
9 26
9 26
9 40
1 51
4 33
1 20
59
1 18
1 05
1 09
1 00
40
57
1 17
1 25
2 38
2 03
3 03
3 32
3 04
3 35
2.8
2.0
3.7
4.3
5.2
4.5
4.7
4.4
5.2
5.4
3.8
3.7
3.2
2.3
3.2
2.9
3.0
2.5
1.7
1.2
2.2
2.6
3.1
2.6
2.8
2.6
3.6
3.4
2.3
2.2
2.1
1.5
2.1
1.9
2.0
1.7
Vineyard Haven: W. Chop lighthouse...
Gay Head: Lighthouse.. .
Cutty hunk: Lighthouse... . ,.
New Bedford: Baptist Church
Sakonnet Point: Lighthouse
Rhode Island.
Beaver Tail : Lighthouse
Newport: Flagstaff, torpedo station
Bristol Ferry: Lighthouse..
Providence: Brown University Obsy
Point Judith: Lighthouse
Block Island : Lighthouse (SE.)
Watch Hill Point: Lighthouse
Montauk Point: Lighthouse
*
fc
d
a
es
fl
w
Stonington: Lighthouse
New London: Groton Monument
Little Gull Island: Lighthouse
Gardners Island: Lighthouse, N. pt
Plum Island: Lighthouse, W. pt
Say brook: Lighthouse, Lynde Pt
10 29
11 08
4 11
4 54
4.3
7.0
2.8
4.9
New Haven: Yale University Obsy. .
APPENDIX IV. [Page 283
MARITIME POSITIONS AND TIDAL DATA.
EAST COAST OF NORTH AMERICA Continued.
l
Place.
Lat. N.
Long. W.
Lion. Int.
Range.
H. W.
L. W.
Spg.
Neap.
N
A
6
1
j
1
8
i
f
i
m
I~*
s
if
*s
I!
jf
|
1
E
K
E
I
j
c
a
h
M
fa
BJ
1
E
i
Bridgeport Harbor* Lighthouse
A. TO.
11 09
11 03
7 48
7 19
5 13
8 44
h. m.
5 04
4 56
1 38
1 20
46
2 49
ft.
8.4
8.2
3.0
2.2
2.8
5.3
6
5.7
2.0
1.4
1.8
3.4
41 09 24
41 02 56
40 51 03
40 37 57
42 39 13
40 42 02
40 42 44
40 36 20
40 27 42
40 28 15
40 23 48
39 45 52
39 30 22
39 21 59
38 47 20
38 55 59
39 58 02
39 53 14
39 44 27
38 46 42
37 54 40
37 23 46
37 07 22
39 17 48
38 58 53
38 02 19
38 52 30
38 55 14
38 53 20
37 00 06
3649 33
37 32 16
36 55 35
36 17 58
36 03 24
36 22 36
35 49 07
35 15 17
35 06 32
35 06 21
34 37 22
34 43 05
33 34 26
33 22 08
33 13 21
33 01 06
32 41 43
32 46 34
32 26 02
32 05 33
32 01 20
32 04 52
31 23 28
31 21 54
31 08 02
31 08 51
73 10 49
73 25 11
72 30 16
73 13 08
73 46 42
73 58 51
74 00 24
74 03 15
74 00 09
73 50 09
73 59 10
74 06 24
74 17 08
74 24 52
74 34 36
74 57 39
75 16 39
75 10 32
75 33 03
75 05 03
75 21 23
75 41 59
75 54 24
76 36 30
76 29 08
76 19 20
76 59 45
77 03 57
77 00 36
76 18 24
76 17 46
77 26 04
76 00 27
76 13 23
76 36 31
75 49 51
75 33 49
75 31 J6
75 59 11
77 02 24
76 31 29
76 39 48
77 49 12
79 16 49
79 10 55
79 22 19
79 52 54
79 55 49
80 40 27
80 33 15
80 50 37
81 05 26
81 17 01
81 25 39
81 23 30
81 29 26
Norwalk Island* Lighthouse
Shinnecock Bav: Lighthouse . ...
Fire Island : Lighthouse
Albany: New Dudley Observatory
New York: Navy-yard flagstaff
City Hall
Fort Wadsworth: Lighthouse
7 41
7 30
1 38
1 23
5.4
5.6
3.5
3.6
Sandy Hook: Lighthouse (rear)
Lightship
Navesink Highlands: N. lighthouse
Barnegat Inlet: Lighthouse
7 50
7 48
9 59
1 43
1 42
3 57
2.7
4.2
4.7
1.7
2.7
3.0
Tuckers Beach: Lighthouse. .
Absecon Inlet: Lighthouse
Five Fathom Bank: Lightship
Cape May: Lighthouse
8J6
1 28
53
12 00
8 17
1 47
8 58
8 02
6 40
1 50
5.6
6.2
7.0
6.7
5.4
3.6
4.4
5.2
4.9
3.5
Philadelphia, Pa.: University Obsy
Navy-yard flagstaff,
League I
Wilmington Del * Town Hall .
Cape Henlopen* Lighthouse..
Assateague Island: Lighthouse... .
Hog Island: Lighthouse
Cape Charles: Lighthouse
8 03
6 34
4 39
31
7 42
2 19
044
10 53
6*2
1 56
3.0
1.4
1.0
1.7
3.5
2.0
1.0
0.8
1.1
2.5
Baltimore: Johns Hopkins Obsy
Annapolis: Naval Academy Observatory.
Point Lookout* Lighthouse
Washington, D. C.: Navy-yard flagstaff...
Naval Observatory. .
Capitol dome
Old Point Comfort Lighthouse
844
9 05
4 30
7 53
2 17
2 47
11 55
1 43
3.0
3.2
4.3
3.2
2.0
2.1
2.9
2.1
Norfolk* Navy-vard fla r staff
Richmond, Va. : Capitol
Cape Henry Lighthouse
Elizabeth City* Courthouse
Edenton : Courthouse
Currituck Beach: Lighthouse
7 37
1 26
3.4
2.2
Bodie Island: Lighthouse
Cape Hatteras: Lighthouse
Ocracoke* Lighthouse
7 00
45
2.2
1.5
Newbern* Episcopal spire
Cape Lookout * Lighthouse
6 29
7 21
20
1 08
4.4
3.3
3.0
2.3
Beaufort N C * Courthouse
Frying-Pan Shoals : Lightship
Georgetown* Episcopal Church
8 39
3 38
4.3
2.9
Lighthouse North I
Cape Romain* Lighthouse
6 59
50
5.9
4.1
Charleston * Lighthouse Morris I
St Michael s Church
7 20
8 10
1 10
2 06
6.0
8.5
4.2
5.9
Beaufort S. C : Episcopal Church
Port Royal: Martins Industry lightship...
Tvbee Island * Lighthouse . . .
7 10
8 13
7 30
7 40
7 30
8 00
1 04
3 07
1 24
1 44
1 27
1 57
7.9
7.6
8.4
7.5
7.5
7.8
5.5
5.3
5.8
5.2
5.3
5.4
Georgia.
Savannah : Exchange spire
Sapelo Island : Lighthouse
Darien* Winnowin * House
St Simon* Lighthouse
Brunswick: Academv
Page 286] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
EAST COAST OP NORTH AMERICA Continued.
o
Place.
Lat. N.
Long. W.
Lun. Int.
Range.
H.W.
L.W.
Spg.
Neap.
Belize.
Sand-Fly Cays Hut S end
ft. m.
ft. TO.
ft.
ft.
16 57 50
16 48 50
17 29 20
16 57 40
16 47 45
16 48 10
16 30 54
16 14 15
15 54 00
15 49 45
15 38 00
15 24 20
15 52 20
15 57 45
16 08 00
15 47 11
15 48 45
15 38 00
15 55 45
16 03 40
15 58 00
16 18 00
16 24 20
16 28 00
18 44 00
17 24 21
15 53 00
16 00 00
15 51 50
15 48 50
15 23 40
15 00 04
16 03 30
15 52 00
15 51 00
15 08 50
15 07 00
14 21 12
16 54 00
15 47 45
14 21 33
14 08 00
14 30 00
13 34 30
13 22 54
12 31 40
12 24 00
12 10 00
12 22 35
12 20 39
11 59 00
12 17 30
12 09 17
10 56 15
10 02 00
10 00 16
88 06 05
88 05 36
88 11 20
88 13 48
88 15 15
88 37 40
88 22 13
88 35 51
88 56 20
88 46 22
89 01 36
89 09 15
88 33 22
88 38 50
88 20 15
88 04 31
87 27 46
86 55 00
85 59 18
86 59 15
86 32 09
86 34 27
86 18 41
85 55 00
84 02 00
83 56 25
85 27 10
85 03 00
84 38 33
84 17 10
83 42 36
83 09 22
83 08 20
82 23 27
82 18 07
82 42 08
82 20 00
82 45 57
80 51 27
79 50 53
80 15 20
81 08 21
81 07 21
80 05 05
81 21 26
81 43 06
81 27 53
81 49 54
83 23 10
83 37 12
83 41 57
82 58 35
83 03 35
83 42 15
83 48 30
83 00 57
South Water Cay Center
Belize* Fort George li^ht
8 00
1 50
1.5
0.8
North. Standin Creek * Entrance . . .
Sittee Point- Cay
Cockscomb Mount: Summit, 4,000 feet...
Placentia/ Point Huts on point
Icacos Point S extreme
Sarstoon River* Entrance
Dulce River Entrance ^V side
9 00
2 50
2.0
1.1
Guat.
Dulce Gulf* Fort St Philip
Izabal
Hospital Bight: Hut, N. pt. of entrance..
Cape Three Points: NW. extreme
Honduras.
Seal Cays: S Cay
Omoa : Entrance
Cape Triunfo: Bluff pt
Con^rehoy Peak * Summit 8 040 feet
Truxillo* Fort
Utilla Island* S Cay
Hog Islands: Highest hill on W islet ..
Roatan: Center of Coxen Cay ...
7 35
1 23
3.5
1.8
Port Royal, NW. pt. of George
Cay
Bonacca Island: Summit, 1,200 feet
8 50
2 38
1.5
0.8
Misteriosa Bank S Point
Swan Islands: Light on W. pt. of west
island
Great Rock Head: Bluff extreme
Cape Camaron
Brewers Lagoon: E.side of entrance. . . .
Patuca River: E side of entrance
Carataska Lagoon: E. side of entrance
Cape Gracias-d-Dios : Lighthouse
10 20
4 07
2.0
1.1
Nicaragua.
Caxones Reef: Great Hobby Islet
Gorda Bank* Gorda Cay
Farrall Rock: Center
Half moon Cay Center
Alargate Reef- E pt
Miskito Cays: S end
Miskito Shore.
Rosalind Bank* NW extreme
Serranilla Bank: Beacon Cay
4 00
4 00
10 13
10 13
2.0
2.0
1.1
1.1
Serrana Bank: Little Cay
Quita Sueno Bank: S. extreme of reef
Spit at N W end
Roncador Cay: S. pt. . . .
Old Providence: Isabel House
St. Andrews Island : S W. cove, Entrance I .
Courtown Cays* Middle Cay
4 00
10 13
1.0
0.5
Albuquerque Bank Smith Cay
Pearl Cays: Colombilla Cay
1 50
8 03
2.0
1.1
Pearl Cays Lagoon: Mosquito Pt
Bluefields: Schooner Pt
1 40
7 52
2.0
1.1
Little Corn Island : Gun Pt
Great Corn Island : Wells N. of Quin Bluff.
Greytown : Lighthouse
1 35
1 00
7 47
7 13
2.0
1.5
i.i
0.8
Mount Cartago- Peak 11 100 feet
B
Port Limon: Monument, Park, opp. P. O.
1 00
7 13
1.6
0.9
APPENDIX IV. [Page 287
MARITIME POSITIONS AND TIDAL DATA.
EAST COAST OP NORTH AMERICA Continued.
i
Place.
Lat. N.
Long. W.
Lun. Int.
Range.
H.W.
L.w.
Spg.
Neap.
i
8
i
i
Carreta Point: Extreme
h. m.
&. m.
A-
ft.
9 38 30
9 26 16
9 25 00
9 14 24
9 20 17
9 14 53
9 17 00
9 10 30
9 06 00
9 19 27
9 22 39
9 22 09
9 33 20
9 34 00
8 53 52
8 46 30
82 39 06
82 20 40
82 19 28
82 19 36
82 14 29
82 07 48
83 03 00
81 54 06
81 33 57
80 00 22
79 57 13
79 54 42
79 39 13
78 57 00
77 40 53
77 32 15
Almirante Bay: Tirbi Pt., Extreme
Columbus I., Lime Pt
Shepherd I., Summit. . . .
Bocaa del Toro, Radio
Tel. Sta
42
Crawl Cay Channel : Crawl Cay
Blanco Peak: Summit, ll,740*feet
Chiriqui Lagoon: Valiente Peak, Summit.
Escudo de Veragua: NW. Pt. of Island . . .
Chagres : San Lorenzo Castle
Toro Point: Lighthouse
Colon : Lighthouse
06
6 18
1.1
0.6
Porto Bello: Ft. St. Geronimo .
Gulf of San Bias: Cape San Bias
Caledonia Harbor: Dobbin Cay. .
11 30
5 17
1.5
0.8
Port Carreto: Peak
WEST COAST OF NORTH AMERICA.
i
X
Point Barrow: Highest lat. of Alaska ....
Icy Cape : Extreme
71 23 30
70 16 00
68 52 00
67 09 00
66 14 30
66 32 00
65 35 30
65 33 30
65 16 40
64 26 00
63 26 00
63 34 30
61 40 00
63 16 00
60 18 00
60 13 00
60 25 22
58 48 31
57 30 24
55 54 59
56 34 23
52 56 01
51 59 04
51 23 39
51 49 18
52 10 36
57 07 19
53 52 54
54 13 30
54 26 12
55 20 45
55 19 17
55 07 36
55 03 17
54 58 25
54 55 30
156 27 00
161 47 30
166 06 00
163 34 00
161 45 00
163 36 00
168 40 00
168 00 00
166 46 30
165 05 00
162 02 30
162 42 30
166 15 00
168 41 00
172 02 00
172 36 00
166 08 30
160 50 00
157 58 30
160 34 54
169 39 50
Long E.
173 12 24
177 30 00
179 12 06
LongW.
176 52 00
174 15 18
170*17 52
166 31 44
162 38 00
162 18 00
160 38 39
160 31 14
159 56 06
159 23 05
159 22 18
159 15 03
11 41
5 33
0.6
0.2
Cape Lisburne : 849 feet
Cape Krusenstern: Extreme
Chamisso Island: Summit.
7 45
1 50
2.0
0.6
Cape Espenberg : Extreme
Diomede Island: Fairway Rock
Cape Prince of Wales: W. pt
Port Clarence: Point Spencer
6 10
[205]
[805]
1 10
[8 25
[1 20;
1.1
[2.11
[4.5J
0.9
Cape Nome : Extreme
St. Michael: Fort
Stuart Island : W. pt
Cape Romanzof : Extreme
St. Lawrence Island : E. pt
St. Matthew Island : SE pt
4 40
11 00
3.1
1.6
Pinnacle Islet: Summit, 930 feet
Nunivak Island : Cape Etolin
Hagenmeister Island
Cape Menchikof : Extreme
PortMoller
St. George Island: S. side
Attu Island : Chichagof Harbor
3 35
3 30
9 48
9 43
5.7
5.2
2.9
2.7
Aleutian Inlands.
Kiska Island: Kiska Harbor, Ast. sta
Amchitka Island: Constantiue Harbor....
Adakh Island : Bay of Islands .
3 25
9 38
5.0
2.6
Atka Island : Nazan Bay (church)
Pribilof Island: St. Paul I., village
4 17
3 50
12 13
10 29
9 58
6 10
2.7
2.9
5.7
1.4
1.5
2.8
Unalaska Island: C. S. station, Ihuliuk. .
Sannakh Reefs: S edge .. ..
Sannakh Island: NE.end
Unga Island
2 40
8 55
8.2
4.1
Popof Island: Humboldt I
Nagai Island : Sanborn Harbor
Koniushi Island: NW. harbor. .
NE. harbor
Simeonof Island : Simeonof Harbor
2 20
8 33
7.5
3.8
61828
Page 288] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
WEST COAST OP NORTH AMERICA Continued.
i
Place.
Lat. N.
Long.W.
Lun. Int.
Range.
H.W.
L.W.
Spg.
Neap.
Alaska.
Cape Strogonof * Extreme
ft. m.
ft. m.
ft.
ft.
56 48 00
56 19 20
56 05 13
55 45 24
55 48 22
57 47 57
60 20 43
59 27 22
60 20 45
59 33 42
58 36 57
57 02 52
58 18 00
56 27 00
54 15 25
54 10 30
52 56 31
52 09 07
51 54 00
53 02 00
53 22 20
54 13 00
54 02 14
54 05 50
49 15 22
49 13 46
48 54 41
48 47 23
49 27 31
49 22 07
49 35 31
49 47 20
49 52 45
49 59 55
50 11 21
50 06 31
50 29 25
50 32 26
50 46 41
50 54 47
50 50 49
50 42 36
50 35 02
49 36 29
49 15 43
49 12 50
49 10 15
48 25 26
48 25 50
48 17 53
48 33 30
54 33 20
54 17 17
50 33 58
50 31 09
50 24 15
50 02 42
49 24 39
158 46 00
158 24 24
156 39 19
157 27 04
155 42 51
152 21 21
146 37 38
146 18 45
141 00 12
139 46 16
137 40 06
135 19 31
134 24 00
132 23 00
133 02 00
133 05 10
132 09 06
131 03 20
131 01 26
131 31 00
131 51 00
131 37 00
132 11 16
132 26 10
125 55 43
124 50 07
125 16 54
125 13 14
126 24 53
126 31 58
126 36 58
126 56 31
126 59 21
127 08 56
127 37 24
127 56 46
128 03 05
127 35 44
128 26 11
127 55 29
127 39 23
127 24 33
126 56 56
124 50 44
124 07 32
123 48 11
123 56 02
123 23 31
123 26 48
123 31 47
124 27 37
130 26 09
130 21 33
126 16 06
126 03 47
125 38 26
125 14 34
123 28 46
OTngnilt Bay Anchorage
Anowik Island* S end
1 45
7 58
8.1
4.0
Lighthouse Rocks
Chirikof Island .
Kodiak Island, St. Paul Harbor: Cove
NW of village
16
50
6 24
7 05
9.0
10.1
4.5
5.1
Port Etches
Middleton Island ....
Mount St Elias* Summit
Yakutat Bay Port Mulgrave
e 34
6 41
9.5
5.0
Lituya Bay
Sitka* Middle of parade ground
06
45
30
6 17
6 56
6 39
9.9
18.6
17.7
5.2
9.7
9.2
Juneau
Wrangell Ast station .
North Island N pt
Queen Cnarlotte Is.
Cape Knox Extreme .
Port Kuper* Sansum I
00
6 12
11.5
6.1
Forsyth Point* Extreme
St James Cape* S extreme
Cumshewa Harbor: N. side of entrance...
Skidegate Bay Rock on bar
07
6 19
12.8
6.7
Rose Spit Point: Extreme
Masset Harbor: Masset village
Cape Edenshaw: Extreme
Hecate Bay Observatory Islet
12 15
45
6 08
7 20
10.0
12.4
5.8
7.1
Vancouver Island.
Stamp Harbor* Observatory Islet
Island Harbor* Observatory Islet
Cape Beale Lighthouse
12 20
12 05
6 15
5 56
9.9
10.3
5.7
5.9
Hesquiat Harbor* Boat Cove
Estevan Point* S extreme...
Nootka Sound : Friendly Cove
12 05
5 55
9.8
5.6
Port Langford : Col wood Islet
Esperanza Inlet: Observatory Rock
11 55
11 50
11 47
5 45
5 38
5 34
9.7
9.3
9.3
5.5
5.3
5.3
Kyuquot Sound : Shingle Point
Nasparti Inlet: Head Beach
Cook Cape* Solander I
North Harbor* Observatory Rock
Hecate Cove: Kitten Islet
Cape Scott: Summit.......
Bull Harbor, Hope Island : N . pt. Indian I .
Port Alexander: Islet in center. .
10
32
30
55
4 45
4 52
6 22
6 44
6 42
7 08
11 00
11 18
10.7
11.6
11.5
12.8
10.6
10.2
5.6
6.1
6.0
6.7
6.6
6.4
Beaver Harbor: Shell Islet
Cormorant I.: Yellow Bluff in Alert Bay.
Baynes Sound* Beak Pt
Nanoose Harbor* Entrance Rock
Nanaimo: Lighthouse
"R fin son s TToiisfi
4 40
[2 171
[2 00]
11 05
[8311
[814]
9.8
[5.71
[5.8J
6.1
Victoria : Lighthouse
Esquimalt : Fisgard I. light .
Race Island Lighthouse
Port San Juan: Pinnacle Rock
Port Simpson : Methodist Church Spire . . .
Prince Rupert Hbr. : Fairview Obs. Spot. .
Port Harvey Tide Pole Islet
15
50
1 55
2 30
3 40
4 45
5 38
20
24,17
14.1
16.0
15.7
7.2
9.0
6.5
16
7.4
8.3
7.7
4.8
5.6
g
d
s
8 10
8 47
10 00
10 15
11 58
Port Neville: Robber s Nob
Knox Bay, Thurlow Island: Stream at
head of bay
Valdes Island : S. pt
Howe Sound: Plumper Cove
:?. I
APPENDIX IV. [Page 289
MARITIME POSITIONS AND TIDAL DATA.
WEST COAST OF NORTH AMERICA Continued.
I
Place.
Lat. N.
Long. W.
Lun. Int.
Range.
H. W.
L.W.
Spg-
Neap.
Washington. Brltlsb Col.
Atkinson Point Lighthouse
ft. m.
5 20
5 28
5 11
ft. m.
11 35
12 01
11 23
h
8.2
7.0
ft.
4.9
5.0
4.4
49 19 42
49 16 18
49 07 04
49 13 01
49 00 00
49 00 00
48 09 19
47 10 20
47 35 54
48 06 56
48 19 07
48 10 52
48 08 24
48 23 30
46 43 00
46 16 29
47 33 43
47 15 32
46 11 19
44 40 35
43 20 36
42 50 22
41 44 36
41 03 01
40 48 11
40 41 37
40 26 18
38 57 12
37 59 39
37 47 28
37 47 30
37 52 24
38 05 56
38 03 05
37 41 51
37 20 49
37 21 03
37 19 58
37 10 49
36 57 31
36 35 21
36 37 55
35 39 50
34 26 49
34 26 10
34 15 46
33 42.14
34 03 05
32 39 48
123 15 54
123 11 26
123 11 27
123 53 52
123 04 52
122 44 56
122 40 34
122 35 51
122 19 59
122 44 58
122 50 36
123 06 31
123 24 07
124 44 06
124 04 25
124 03 11
122 37 59
122 26 26
123 49 42
124 04 40
124 22 31
124 33 30
124 12 10
124 09 03
124 09 41
124 16 26
124 24 25
123 44 27
123 01 24
122 25 43
122 27 49
122 **-**
***,
122 16 24
122 09 23
123 00 07
121 56 26
121 36 40
121 53 39
122 23 39
122 01 29
121 52 59
121 56 02
121 17 06
120 28 18
119 42 42
119 15 56
118 17 41
118 14 32
117 14 37
117 09 41
117 07 32
120 21 55
119 58 29
119 33 51
119 23 04
119 02 29
119 31 19
118 24 05
Vancouver, Burrard Inlet: Govt. Re
serve, English Bay
Fraser River* Garry Pt
New Westminster: Military barracks
Point Roberts : Parallel station
Semiamoo Bay : Parallel station
4 59
11 10
7.1
4.6
Admiralty Head : Lighthouse
Steilacoom : Methodist Church
4 46
4 22
3 47
3 40
2 42
2 10
08
11 04
10 33
9 32
9 28
8 34
8 23
6 16
11.0
9.2
6.2
5.6
5.0
5.3
7.1
7.2
6.0
4.0
3.7
3.3
3.4
4.1
Seattle C S ast station
Port Townsend * C S ast station
Smith Island: Lighthouse..
New Dungeness: Lighthouse
Port Angeles : Ediz Hook lighthouse . .
Cape Flattery: Lighthouse
Cape Shoal water: Lighthouse
Cape Disappointment: Lighthouse
12 22 i 6 19
4 27 10 35
4 32 10 45
15 6 42
11 50 ! 5 37
11 55 ! 5 49
7.7
9.4
9.8
7.8
7.3
6.0
4.5
6.1
6.4
4,7
4.3
3.5
Bremerton Navy-yard flagstaff
Tacoma- St Luke s Church
Astoria: Flagstaff
Oregon.
Yaquina Head : Lighthouse
Cape Arago, or Gregory: Lighthouse
Cape Blanco : Lighthouse
Crescent City : Lighthouse
11 33
11 27
11 57
11 33
11 00
10 36
11 23
12 07
11 43
5 15
5 11
5 45
5 19
4 50
4 21
5 08
5 34
5 07
5.8
5.7
5.7
5.3
4.7
4.1
5.1
5.1
4.9
3.4
3.3
3.3
3.1
3.0
2.6
3.2
3.2
3.1
California. >
Trinidad Head : Lighthouse
Eureka: Methodist Church
Humboldt Lighthouse
Cape Mendocino* Lighthouse
Point Arena: Lighthouse
Point Reyes: Lighthouse. ..
San Francisco: Davidson Observatory...
Presidio
Berkeley Univ. Obsy
Mare Island: Chronom. and Time Sta.,
Navy-yard
5
Hi
1 OO
10 40
7 15
7 48
4 25
5.6
5.6
4.5
3.7
3.7
2.9
Benicia* Church
Farallon Islet Lighthouse
Santa Clara: Catholic Church
Mount Hamilton: Obs. peak
San Jose : Spire
Pigeon Point : Lighthouse
Santa Cruz : Warehouse flagstaff
10 54 4 27
10 43 4 24
5.2
4.8
3.3
3.1
Monterey: C. S. azimuth station
Point Pinos: Lighthouse
Piedras Blancas: Lighthouse
Point Conception: Lighthouse
Santa Barbara: N. tower, Mission Church.
San Buenaventura: C. S. ast. station
Pt. Fermin, San Pedro Bay: Lighthouse..
Los Angeles: Courthouse
9 37 ! 3 io
9 53 3 21
9 36 3 13
4.8
4.9
5.5
2.2
2.2
2.5
Point Loma Lighthouse
9 29 3 07
9 32 3 20
5.2
5.1
2.3
2.3
San Diego: C. S. ast. station
32 43 06
32 31 58
34 04 19
33 56 30
34 03 12
34 00 25
33 28 16
33 14 55
33 23 09
Mexican Boundary: Obelisk
San Miguel Island : Seal Pt
9 23
3 02
4.9
2.2
Santa Rosa Island: E. pfc
Santa Cruz Island : NE pt
9 29 3 06
4.9
2.2
Anacapa Island: E. pt .
Santa Barbara Island : Summit
San Nicolas Island: Summit
9 20
9 28
3 04
3 08
4.9
5.1
2.2
2.3
Santa Catalina Island : Ca talma Peak
Page 290] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
WEST COAST OP NORTH AMERICA Continued.
I
Place.
Lat.N.
Long. W.
Lun. Int.
Range.
H. W.
L.W.
Spg.
Neap.
Lower California.
Ensenada Harbor: Head of bay, close to
beach. ....
h. 771.
9 28
h. m.
3 06
ft.
5.0
ft.
2.2
31 51 10
31 33 04
30 57 39
30 28 58
30 22 16
29 47 20
29 25 29
29 10 50
28 56 06
28 40 16
28 14 26
28 03 52
28 18 08
27 39 35
27 06 10
26 45 45
26 42 49
26 18 56
26 03 18
24 58 00
24 47 31
24 38 23
24 18 12
24 20 17
23 27 14
22 53 07
23 03 35
23 32 48
24 03 52
24 15 31
24 10 10
24 24 10
24 52 03
25 29 23
25 59 37
26 00 41
26 30 44
26 53 37
27 10 21
27 26 06
28 00 07
28 25 04
28 47 40
28 49 11
28 56 39
29 13 52
29 33 08
29 57 27
30 25 16
31 02 57
31 46 10
31 00 54
30 16 05
29 54 12
29 16 12
28 45 55
28 45 28
28 03 22
27 50 28
116 38 05
116 40 51
116 17 28
116 06 46
115 59 07
115 48 12
115 12 14
118 18 30
114 31 06
114 14 15
114 06 21
115 11 32
115 36 10
114 54 27
114 17 25
113 16 25
113 35 04
112 41 44
112 17 52
115 51 54
112 18 25
112 08 54
111 42 54
111 30 21
110 14 07
109 54 50
109 40 43
109 28 57
109 50 29
110 20 34
110 20 41
110 20 35
110 41 47
111 01 43
111 06 53
111 21 03
111 27 14
111 58 04
112 05 39
112 19 56
112 47 36
112 51 59
113 12 48
113 00 05
113 34 35
113 40 00
113 35 19
114 25 49
114 39 47
114 52 10
114 43 31
113 16 30
112 53 26
112 45 04
112 28 51
112 21 46
111 58 37
111 16 00
110 54 28
San To mas* NW shore of cove
Colnett Bay: Head of bay
9 27
3 05
5.8
2.6
San Martin Island* Hassler Cove
Port San Quentin Sextant Pt
9 23
3 00
4.9
2.2
San Geronimo Island: Bight at E. end. . .
Canoas Point* High bluff .
Guadeloupe : North pt
La Playa Afaria* Mound on W side
9 15
2 53
7.6
3.4
Santa Rosalia Bay Obs spot Cairn
Lagoon Head* Highest pt of crater.
Cerros Island * SE extremity
9 05
2 42
7.8
3.5
San Benito Island : Summit of W. island. .
San Bartolome"* N side of entrance
9 00
2 37
8.2
2.8
Asuncion Island* Summit of island
San Ignacio Point* Extreme
Abreojos Point: Extreme of rocky ledge..
San Domingo Point: Edge of cliff
9 00
2 48
6.7
2.3
San Juanico Point* Knoll
8 29
2 17
5.7
1.6
Alijos Rocks* South Rock
Cape San Lazaro* Extreme
Magdalena Bay: Obs. spot (post) N. of
Port Magdalena
8 25
2 12
5.5
1.5
Cape Tosco * Extreme . ...
El Conejo Point: Extreme
Todos Santos: Foot of hill, Lobos Pt
San Lucas: Steep sand beach, NW. pt. of
bay
San Jose" del Cabo: NE. side of entrance. .
Arena Point* Extreme
8 36
2 20
4.5
1.2
Arena de la Ventana* Extreme
Pichilinque Bay: SE. pt. of San Juan,
Nepomezeino I
La Paz: Obs. spot, El Mogote.
9 40
3 34
5.4
1.3
Lupona Point: Extreme
San Evaristo: 3m. S. of S. Evaristo Hd. .
San Marcial Point* Extreme
Salinas Bay: Beach, NE pt of bay
Loreto: Cathedral
Pulpito Point: Summit
Muleje: Equipalito Pt
San Marcos Island: S. sand spit
Santa Maria Cove: Beach on NW. shore. .
San Carlos Point: Extreme
Santa Teresa Bay: Beach on N side
11 50
5 47
11.2
2.6
Las Animas: Low pt
Raza Island: Landing place, S. side
Angeles Bay: Bight on NW. shore
Remedies Bay: Beach on W. shore
Mejia Island: S. side
San Luis Island: SE. side
San Firmin: Beach, N. of bight
San Felipe Point: Peak, 1,000 feet
Philips Point: Beacon
Georges Island: NE. shore
Mexico.
Cape Tepoca: Hill, 300 feet
Libertad Anchorage: Beach
Patos Island: SE. end
Tib uron Island: SE. end
Kino Point: 0.2 mile N. 88 W. of mound. .
San Pedro* N side of bay
Guaymas: Lighthouse
11 30
5 26
5.0
1.2
APPENDIX IV. [Page 291
MARITIME POSITIONS AND TIDAL DATA.
WEST COAST OF NORTH AMERICA Continued.
j
o
i
g
Place.
Lat. X.
Long. TV.
Lun. Int.
Range.
H.W.
L.W.
Spg.
Neap.
Claris Island: NW part
ft. m.
ft. 771.
ft-
ft.
26 58 59
26 41 09
26 16 35
25 33 56
25 23 06
25 11 42
24 38 52
23 10 40
22 30 26
21 32 30
21 30 45
20 45 50
20 36 26
20 25 00
19 34 48
19 17 15
18 42 57
18 59 41
18 20 55
10 17 00
19 13 25
19 03 15
17 58 21
17 40 15
17 37 50
17 31 28
17 16 13
16 49 10
16 19 37
15 39 09
15 40 41
15 44 58
15 52 17
16 09 36
14 17 44
13 55 15
13 34 20
13 28 50
13 20 00
13 17 09
12 27 54
11 14 45
11 03 10
10 36 46
9 43 45
8 10 13
8 04 30
7 43 32
7 24 20
5 32 57
8 57 06
8 47 45
7 27 40
4 03 00
8 39 00
8 54 30
8 56 32
8 12 30
8 28 50
109 57 17
109 40 48
109 17 30
109 10 23
108 49 00
108 23 37
107 59 37
106 26 47
105 44 25
105 18 40
106 33 14
105 33 37
105 16 00
105 39 21
105 08 54
110 49 22
110 56 53
112 04 07
114 44 17
109 13 00
104 43 26
104 19 50
102 07 06
101 40 25
101 33 23
101 27 14
101 04 32
99 55 50
98 35 05
96 30 43
96 15 04
96 08 10
95 46 43
95 12 16
91 55 36
90 49 45
89 50 26
89 19 20
87 51 00
87 47 06
87 12 31
85 53 00
85 43 38
85 42 46
85 00 46
82 14 32
81 43 30
81 31 58
81 41 51
86 59 17
79 32 09
79 33 16
79 59 25
81 36 00
79 41 45
79 31 15
79 07 55
78 54 40
78 05 35
Santa Barbara* NW side of bay
A^iabampo* SE side of entrance
Topolobampo: SE. end of Santa Maria I..
Navachista* W side of creek
Playa Colorado* N side of entrance
^.Itata* N side of entrance
10 07
9 08
3 59
2 51
5.8
3.8
1.4
0.9
Mazatlan* Lighthouse
Palenita \~illage* Boca Tecapan
San Bias* Customhouse
9 08
2 52
3.2
1.0
Maria Madre Island* SE extreme
Mita Point* Extreme
Penas Anchorage* Mouth of Rio Real
Cape Corrientes* Extreme ..."
Perula Bay Smooth Rock .
9 07
2 53
2.5
1.1
San Benedicto Island: S. extreme ...
Socorro Island: SE. part
Roca Partida* Summit
Clarion Island* S end
Clipperton Island* Summit
Navidad Bay: W. end of sandy beach
Manzanilla Bay: Flagstaff, U.S. consulate.
Sacatula River: Beach, W. side of bay
Isla Grande: Tripod on NW. summit
9 07
2 54
1.9
L3
Sihuatanejo Point* Tree on beach
8 50
2 38
2.0
0.9
Morro Petatlan: Junction of stony and
sandv bea.ch.es
Tequepa Harbor* Limekiln
Acapulco* Lighthouse .
Maldonado* El Recordo Pt ....
Port \ngeles : Lighthouse
Sacrificios Point: Highest pt. of cape. . . .
Port Guatulco* Cross
Morro Ayuca: Summit of N. edge of cape.
Salina Cruz* Lighthouse
Champerico: Inshore end of iron wharf...
San Jose de Guatemala: Lighthouse
2 50
2 50
2 55
3 05
3 15
9 02
9 02
9 08
9 18
9 28
8.5
9.0
9.5
10.0
10.5
4.6
4.9
5.1
5.4
5.7
1 Contra! America.
\caiutla* Lighthouse
Libertad* Lighthouse
La Union 1 Lighthouse
Chicarene Point Extreme
Corinto* Lighthouse
2 55
3 00
2 50
2 45
9 08
9 12
9 02
8 58
10.5
10.0
9.5
9.0
5.7
5.4
5.1
4.9
San Juan del Sur: Signal station
Salinas Bay: Salinas Islet
Port Culebra: Extremity of Mala Pt
Ballena Bay: N. Estero Toussa
Parida Anchorage* S pt of Deer Id
3 15
9 28
10.5
5.7
Port \uevo* Entrada Pt
Bahia Honda: W. end of Centinela I. . . .
Coiba (Quibo) Island: Observation pt
Cocos Island: Head of Chatham Bay. . . .
Panama : Cathedral, S. tower
3 10
9 22
11.0
5.9
3 00
3 00
3 10
9 14
9 13
9 22
16.0
15.4
13.0
8.7
8.3
7.0
Taboga Island : Church ....
Cape Mala: Extreme
Malpelo Island* Summit
Point Cham6* Extreme
3 30
9 42
15.0
8.1
Flamenco Island: N Pt
Chepillo Island: Center
3 05
3 00
9 18
9 13
16.0
15.7
8.7
8.5
Rev Island: Cocas Pt. extreme
Darien Harbor: Graham Pt
Page 292] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
WEST INDIA ISLANDS.
I
Place.
Lat. N.
Long. W.
Lun. Int.
Range.
H.W.
L.W.
Spg.
Neap.
ii
d
M
J
3
A
i
cS
A
w
Memory Rock* Center . . . .
ft. ra.
7 40
h. m.
1 28
ft.
3.2
ft.
1.7
26 56 53
26 41 18
25 51 30
26 31 10
27 15 42
26 02 00
25 34 30
22 45 10
22 22 30
21 42 00
22 01 15
22 14 02
22 20 44
22 31 15
22 51 00
23 32 15
23 06 00
25 00 00
25 31 20
25 05 37
24 43 45
25 49 40
25 49 12
24 06 15
23 50 50
23 56 40
23 37 45
22 06 40
22 32 40
22 47 30
22 51 00
23 05 30
22 34 38
22 16 30
21 40 30
20 56 00
21 30 40
21 37 30
21 30 00
21 54 00
21 29 33
21 30 55
21 06 30
20 35 00
20 02 00
20 15 00
20 21 46
20 41 41
20 47 19
21. 04 24
21 09 00
21 07 00
21 07 30
21 07 15
21 18 30
21 32 44
21 40 02
22 08 45
22 11 14
22 29 10
22 09 44
22 38 41
79 06 54
79 00 38
77 10 45
76 57 36
78 23 48
79 06 00
79 18 26
78 06 02
77 34 26
75 44 39
75 10 34
75 45 17
75 28 20
75 51 41
74 51 54
75 46 24
74 59 00
76 13 00
76 51 48
77 21 58
77 46 45
77 53 55
77 57 06
74 26 00
75 07 27
74 28 20
74 50 08
74 20 37
74 22 54
74 20 21
74 22 48
73 49 15
73 38 03
72 47 03
73 50 29
73 40 17
73 42 33
72 28 18
72 12 51
72 07 14
71 31 12
71 07 29
70 29 54
69 21 24
68 47 24
74 08 01
74 29 13
74 53 44
75 34 21
75 36 59
75 47 18
75 47 40
75 52 18
76 06 27
76 35 34
77 15 18
77 08 04
77 37 33
77 39 23
78 09 11
78 35 54
79 13 44
Htihaniii Island * W pt
Abaco Island. * Lighthouse
Little Guana, Cay Lighthouse
Walker Cay * Highest part
Great Isaac Cay* Lighthouse
Gun Cay Lighthouse
8 20
2 08
3.0
1.5
Ginger Cay Center
Cay Lobos" Lighthouse
St Domingo Cay Center
Cay Verde* Hill at S end
Ragged Island * Gun Pt
Nairn Cay E pt
Nurse Channel Cay Beacon
Long Island* S pt
Great Exuma Island* Beacon
Clarence Harbor: Lighthouse
8 20
7 00
2 08
48
4.1
4.0
2.1
2.1
Eleuthera Island: Lighthouse
Royal Island: Eastern Pass.. . . ..
Nassau: Lighthouse
7 20
7 40
1 08
1 28
4.0
3.0
2.1
1.5
Andros Island : Lighthouse .
Great Stirrup Cay Lighthouse
Little Stirrup Cay W end
San Salvador (Cat I.) : Lighthouse
7 00
48
4.0
2.1
Concepcion Island* W bay
Watlings Island: Hinchinbroke Rock
Rum Cay: Harbor Pt
Castle Island: Lighthouse
Fortune Island: S end
Crooked Island: Moss flagstaff
Bird Island: Lighthouse
Samana Cay: W. pt
Plana Cay NW pt
Mariguana Island: SE.pt
7 20
1 08
3.0
1.5
Hogsty Reef* NW Cay
Inagua Island: Lighthouse.
7 50
1 38
3.5
1.8
Little Inagua Island* NW pt
W. Caicos Cay: Hill SE end
French Cay: W. pt
Fort George Cay: Old magazine
Caicos Island: Parsons Pt S islet
Turk Island: Lighthouse
7 30
1 18
3.0
1.5
Square Handkerchief Bank: NE. breaker.
Silver Bank* E extreme
Navidad Bank* Center of E side
Cape Maysi: Lighthouse
5 40
11 53
2.8
1.6
Port Baracoa: Lighthouse
Port Cayo Moa: Carenero Pt
Nipe Bay: Extremity of Carenero Pt
Lucrecia Point: Lighthouse
Port Sama: E. side of entrance
Peak of Sama: Summit, 885 feet
Port Naranjo* E side of entrance
Gibara: Lighthouse
6 20
08
2.4
1.4
Port Padre* Guinchos Pt
Port Nuevitas: NW. corner R. R. station.
Maternillos Point: Lighthouse
7 00
48
2.2
1.2
Cay Verde: NW. end
Cay Confites * S pt
Paredon Grande Cay: Lighthouse. . .
7 20
1 08
2.8
1.6
San Fernando : NW. corner Old Spanish
Fort No 1
Cayo Frances* Lighthouse
i
APPENDIX IV. [Page 293
MARITIME POSITIONS AND TIDAL DATA.
WEST INDIA ISLANDS Continued.
1
Place.
Lat. N.
Long. W.
Lun. Int.
Range.
H.W.
L.W.
Spg.
Neap.
ci
i
5
Isabella deSagua: SE. corner of church ..
Cav Sal Lighthouse
h. m.
h. m.
ft.
ft.
22 56 30
23 56 30
23 12 34
23 14 10
23 02 43
23 01 54
23 09 26
23 09 04
23 09 11
22 59 11
23 00 00
22 29 32
21 52 01
21 53 55
22 14 36
21 55 00
21 35 30
22 41 09
21 57 45
22 01 49
22 08 36
22 06 52
21 48 16
21 37 24
20 42 23
20 20 26
20 02 55
19 50 32
19 53 31
19 56 57
19 57 29
19 54 42
19 53 04
19 57 00
19 54 08
20 01 01
19 45 15
19 39 10
19 17 45
18 33 00
17 55 05
18 11 31
18 23 00
18 26 24
18 30 34
18 29 25
18 27 45
18 12 20
17 55 56
17 55 56
17 26 30
17 06 20
15 53 00
18 35 52
19 12 29
19 22 12
19 48 51
19 54 00
19 46 20
19 46 19
80 00 32
80 27 51
80 29 26
81 07 20
81 12 02
81 43 18
82 21 29
82 20 38
82 21 01
83 09 13
83 13 00
84 14 17
84 57 09
84 56 16
83 34 24
83 31 18
83 09 13
82 17 42
81 07 18
80 26 32
80 27 05
80 27 11
79 58 58
78 51 13
77 59 45
77 07 33
77 34-50
77 43 33
Bahia de Cadiz Cay Lighthouse. .
Piedras Cav Lighthouse
Cardenas * Cross on Cathedral
Matanzas * Summit of peak
8 30
8 18
2 18
1 56
2.2
1.3
1.2
0.7
Habana * \Iorro lighthouse
Transit pier, Casa Blanca Ob
servatory
Flagstaff Cabanas Fortress
Bahia Honda : SE . corner Morillo Fort
Gobernadora Pt. : Lighthouse
Dimas N\7 corner of warehouse
Cape San Antonio Lighthouse
8 30
2.18
1.5
0.9
Radio tower
La Caloma: SW. corner of warehouse
San Felipe Cays- SW pt
Isla de Pinos* Port Frances . .
Batabano Lighthouse
Piedras Cay : Lighthouse
Cienfuegos: Colorados Pt. light
4 47
11 00
2.0
1.1
Cathedral tower
Flagstaff Punta Gorda
.
Casilda* Observation pier
Jucaro Observation pier
1
Santa Cruz del Sur: Observation pier
Manzanillo Observation pier
Niniie^O Siigar mill Rmokestarlc
Cape Cruz* Lighthouse
Point Mota
Chirivico * Damas Cay . ...
Santiago * Lighthouse
75 52 03
75 09 28
75 09 28
75 07 33
75 03 08
74 50 49
79 46 07
80 07 17
81 23 17
75 44 24
76 11 08
76 26 31
76 54 22
77 12 52
77 39 52
77 56 16
78 10 52
78 08 54
76 50 35
76 50 38
75 58 20
77 26 28
78 39 04
68 18 50
69 19 23
69 12 12
70 41 27
71 40 15
71 46 40
72 12 07
8 20
7 50
2 30
2 00
2.2
2.6
1.1
1.3
Guantanamo Bay * Fisherman Pt
Lighthouse
Naval Station flagstaff.
Port Escondido Inner Entrance Pt
Port Baitiqueri* Barlovento Pt
Cayman Brae E pt
Little Cayman: w pt
Grand Cayman: Fort George, W. end. . . .
Formigas Bank : Shoal spot
[1.3]
Jamaica.
Morant Point : Lighthouse
fLll
Port Antonio Folly Pt Light
Port Maria N W wharf
St Ann Bay* Long wharf
[1.2]
Falmouth : Fort
Montego Bay : Fort
St. Lucia: Fort
Savanna-la-Mar: Fort
Kino ston Port Royal flagstaff
PortRoval: Fort Charles, flagstaff
ri.il
Morant Cays: NE. Cay
1 Isl. of Haiti.
Pedro Bank Portland Rock E end
Baxo Nuevo Sandy Cay
Cape Enganoi Extreme.. . .
Samana Town: Obs. spot
9 00
2 48
3.0
1.5
Cape Cabron* East extreme
Port Plata: Lighthouse
Monte Cristi" Cabra Island
.Manzanillo Point
6 50
39
5.5
2.9
Cape Haitien Town fountain
1
Page 294] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
WEST INDIA ISLANDS Continued.
i
Place.
Lat. N.
Long. W.
Lun. Int.
Range.
H.W.
L.W.
Spg.
Neap.
Island of Haiti.
Port Paix: Wharf.
ft. m.
ft. m.
ft.
ft.
19 57 06
19 49 15
19 27 12
18 56 00
18 48 50
18 33 31
18 39 15
18 36 48
18 25 00
18 11 08
18 13 25
17 46 08
17 36 55
17 37 37
17 28 22
18 08 55
18 12 13
18 27 54
18 11 57
18 05 17
18 12 37
18 24 51
18 28 23
18 23 01
17 57 10
18 18 56
18 05 54
18 20 23
18 18 08
18 25 04
18 30 39
18 45 11
18 36 30
17 45 09
17 44 43
18 35 37
18 16 42
18 13 06
18 04 07
17 53 58
17 39 10
17 29 10
17 18 12
17 13 38
17 07 52
17 35 50
17 00 00
17 06 54
16 55 18
16 42 12
15 59 50
16 25 09
16 11 57
16 13 14
16 13 56
16 19 56
16 10 17
15 52 59
15 51 32
72 50 00
73 23 07
72 43 52
73 18 20
72 39 13
72 21 00
74 06 52
74 25 50
75 01 57
73 44 08
72 30 45
71 41 06
71 31 10
71 41 10
71 38 30
71 02 25
70 32 53
69 52 59
68 45 41
67 50 50
67 09 17
67 09 42
66 07 26
65 37 07
66 54 13
65 13 40
65 25 26
64 55 47
64 42 03
64 36 47
64 21 48
64 24 58
64 10 45
64 42 16
64 41 14
63 28 13
63 16 00
63 04 39
63 05 45
62 51 30
63 15 16
62 59 09
62 43 14
62 35 25
62 37 29
61 49 54
61 46 07
61 55 11
62 19 10
62 13 24
61 44 09
61 32 15
61 29 40
61 32 05
61 33 15
61 00 44
61 06 45
61 19 15
61 35 55
St. Nicholas Mole: Fort George, flagstaff. .
Gonaives: Verreur Pt
Gonave Island: W. pt
Arcadins Islands: Lighthouse
Port au Prince* Fort Islet light
[1.2]
Jeremie Fort - . .
Cape Dame Marie : Extreme
Navassa Island: NW. extreme
Aux Cayes: Tourterelle Bat y
Jacmel: Wharf
[2.5]
False Cape: Extreme
Beata Island: NW. pt
Fraile Rock: Center
Alta Vela: Summit
Avarena Point: Extreme
Salinas Point (Caldera) : Extreme
Sto Domingo City : Lighthouse
[2.2]
Saona Island : Pt. Catuano
Mona Island: Lighthouse
Porto Rico.
Mayaguez* Mouth of Mayaguez R
7 04
2 00
2.0
1.0
Aguadilla: Columbus Monument
San Juan : Morro lighthouse ....
8 21
2 20
1.3
0.9
Cape San Juan: Lighthouse..
Guanica: Meseta^Pt. lighthouse
1 0]
Culebrita Island: Lighthouse
[731]
[735J
[711]
[130]
[140]
[058]
101
1.1;
[1.2]
Vieques (Crab) Island: Port Ferro light..
St. Thomas: Fort Christian, SW. bastion. .
St. John Island: Ram Head
Tortola: Fort Burt
Virgin Gorda: Vixen Pt
Anegada* W pt
E extreme of reefs
St. Croix, Christiansted: SW. bastion of
fort
St. Croix, Lang s Observatory.
Sombrero : Lighthouse
Dog Island: Center
Anguilla: Customhouse
St. Martin : Fort Marigot light
St Bartholomew: Fort Oscar
[1.5]
Saba: Diamond Rock..
St. Eustatius: Fort flagstaff
St. Christopher: Basseterre Church
Bobby Island : Center
Nevis : Fort Charles
Barbuda: Flagstaff , Martello Tower
Antigua, English Harbor: Flagstaff, dock
yard
[2.0]
Sandy Island: Lighthouse
Redonda Islet: Center. .
Montserrat: Plymouth Wharf
Guadeloupe, Basseterre: Light on mast. . .
Port Louis: Light on mast. .
Gozier Islet: Lighthouse
Manroux Id. : Lighthouse. . .
Point a Pitre: Jarry Mill
Desirade: E. pt
[1.3]
Petite Terre: Lighthouse
Marie Galante: Lighthouse
Saintes Islands: Tower on Chameau Hill . .
APPENDIX IV. [Page 295
MARITIME POSITIONS AND TIDAL DATA.
WEST INDIA ISLANDS Continued.
Place.
Lat. N.
Long. W.
Lun. Int.
Range.
H. W.
L. W.
Spg.
Neap.
Dominica, Prince Ruperts Bay: Sand
beach W of church. . .
ft. m.
4 00
ft. m.
10 12
ft.
1.5
ft.
0.8
15 34 34
15 17 27
15 42 00
14 35 44
14 43 54
14 46 13
14 23 23
14 01 54
13 05 43
13 02 45
13 09 40
13 09 19
13 00 25
12 03 02
11 10 08
11 25 02
11 19 00
10 59 43
10 57 45
11 47 57
11 56 16
12 02 06
11 59 30
12 06 58
12 06 15
12 31 05
61 28 14
61 23 52
63 37 46
61 04 30
61 11 09
60 53 20
60 52 33
61 00 48
59 37 16
59 31 50
59 26 04
61 14 34
61 14 09
61 45 06
60 42 38
63 05 48
63 36 00
63 48 00
65 26 38
66 12 31
66 39 10
68 14 10
68 39 19
68 55 48
68 56 17
70 02 34
Roseau: Flagstaff , Fort Young
Aves Island Center ,
Martinique, Fort de France: Fort St.
Louis light
St. Pierre: Ste. Marthe Bat
tery
Caravelle Pen.: Lighthouse.
Cabrit Islet: Summit
3 50
10 02
1.1
0.6
St Lucia, Port Castries: Lighthouse
Barbados, Bridgetown: Flagstaff, Rick-
ett s Battery
2 50
9 02
3.0
1.5
S Point Lighthouse
Ragged Point: Lighthouse .
St Vincent, Kingstovm : Lighthouse . . .
2 50
9 05
1.6
0.8
Bequia Island, Admiralty Bay: Church. .
Grenada: St. George Lighthouse
2 30
3 50
8 42
10 02
1.5
2.1
6.8
1.1
Tobago Rocky Bay Lighthouse
Testigos Islets: Center of Testigo Grande.
Sola Island: Center . ...
Pampatar, Margarita I.: San Carlos Castle.
Tortugas Island: S. end of W. Tortugillo
Islet
Orchila Island: S. side
Roques Islands: Pirate Cav
Bonaire Island: Lighthouse
Little Curacao Island: Lighthouse
Curacao Island : Fort Nassau
Lighthouse
Oniba Island : Lighthouse
1
NORTH AND EAST COASTS OF SOUTH AMERICA.
Colombia.
Caribana Point: Extreme . . ...
8 37 30
9 24 00
9 24 00
10 25 50
11 00 15
10 07 00
11 15 28
11 33 30
12 12 34
12 23 09
12 04 00
10 57 30
11 48 56
12 11 00
12 29 15
11 27 56
10 47 00
11 10 00
10 29 53
10 36 57
10 35 00
10 34 06
10 49 30
10 13 30
10 27 20
10 40 00
10 42 00
76 52 55
76 10 45
75 48 00
75 32 50
74 57 55
74 49 51
74 14 33
72 54 50
72 09 42
71 45 42
71 07 55
71 37 00
70 17 21
70 04 55
70 57 00
69 34 20
68 19 55
68 22 54
68 00 55
66 56 06
66 06 15
66 04 13
66 09 25
64 44 00
64 11 33
64 17 55
63 50 25
Fuerte Island: N. extreme
. . . |
Cispata Port: Zapote Pt
Cartagena: Lighthouse
Savanilla: Lighthouse
Magdalena River: NW. pt. of Gomez I. . .
Santa Marta: Lighthouse
1
Rio de la Hacha : Li^ht on church
i
Cape La Vela: Sand beach inside cape. . .
Bahia Honda: E. pt., S. side
j
Espada Point: Extremet
1 Venezuela.
Maracaibo : Zapara I lio ht .
5 05
11 17
2.5
1.5
Estangues Point: 500 ft. from extreme
Cape San Roman* Extreme
Marjes Islets* N islet
Vela de Coro: Lighthouse
Tucacas Island: Ore house
St Juan Bay Cay
Puerto Cabello: Lighthouse
La Guaira: Lighthouse
6 00
12 12
2.8
1.7
Cape Codera* Morro
Corsarios Bay: W pt
Centinela Islet: Center.
Barcelona* Morro
Cumana: Lighthouse
Escarceo Point" Extreme
Chacopata* Morro
Page 296] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
NORTH AND EAST COASTS OF SOUTH AMERICA Continued.
i
Place.
Lat. N. ,
Long. W.
Lun. Int.
Range.
H. W.
L.W.
Spg.
Neap.
Venezuela.
Esmeralda Islet Center .
A. ra.
Ji. m.
ft.
ft.
1-0 40 00
10 40 15
10 42 00
10 43 27
10 45 00
10 44 19
10 43 48
10 38 15
8 39 25
10 38 37
10 40 03
10 50 02
10 03 29
10 16 59
6 49 20
5 58 30
5 49 30
5 44 50
5 16 50
5 02 40
4 56 20
4 49 30
4 23 20
4 20 45
2 46 30
1 40 17
Lat. S.
17 00
1 26 59
35 03
2 10 11
2 31 48
2 16 22
2 41 55
2 53 20
3 42 05
4 25 35
5 03 15
5 29 15
5 45 05
. 5 46 41
6 56 30
7 06 35
8 00 50
8 03 22
8 20 45
8 43 40
9 39 35
10 30 30
10 58 20
11 09 45
11 27 40
12 12 05
12 33 40
13 00 37
12 52 48
13 22 37
13 56 42
14 17 40
63 31 55
63 18 00
63 14 00
63 09 43
62 41 55
62 44 29
61 50 50
61 51 18
60 10 15
61 30 35
61 45 54
60 54 10
61 55 41
61 28 12
58 11 30
57 00 30
55 08 48
54 00 30
52 34 53
52 21 11
52 20 26
51 55 36
51 50 36
51 27 46
50 54 46
49 56 46
48 23 30
48 30 01
47 20 54
44 25 56
44 18 45
43 37 30
42 18 02
41 40 35
38 28 25
37 44 55
36 02 52
35 15 52
35 11 55
35 12 43
34 49 30
34 53 04
34 50 36
34 51 57
34 56 05
35 05 06
35 44 54
36 21 51
37 04 00
37 12 36
37 24 00
37 45 46
38 02 16
38 32 06
38 41 28
38 54 38
39 07 05
39 00 45
Carupano: Lighthouse
Pt Herman Vasquez
Puerto Santo Bay: Sand spit S. of Morro.
Tres Puntas Cape* Extreme
Unare Bay: Obs. spot, 200 yds. S. of Morro.
Pena Point Extreme
Pato Island* E pt
Mocomoco Pt Extreme
Port of Spain* King s Wharf light
4 20
10 30
3.2
1.9
Trinidad.
Chacachacare Island: Rocks off SW. pt. .
Galera Point: NE. extreme, lighthouse...
Icacos Point* Lighthouse
San Fernando* Pierhead
Demerara* Georgetown lighthouse
4 18
9 50 8. 6
3.9
Oulana.
Nickerie River* Lighthouse .
Paramaribo* Stone steps . .
5 50
12 66 9. 5
4.3
Maroni River* W lighthouse
Salut Islands: Lighthouse
Enfant Perdu Islet* Lighthouse
i
Cayenne: Lighthouse
4 27
10 30
6.0
2.7
Connetable Islet* Center
Carimare Mount* Summit
Orange Cape * Extreme
Brazil.
May e Mountain: Summit
North Cape: Extreme
Cape Magoari: Extreme
Para: Customhouse
11 50
5 37
11.0
5.2
Atalaia Point* Lighthouse
Itacolomi Point* Lighthouse
Maranhao Island: Landing place
6 50
5 35
5 05
38
11 47
11 17
16.5
13.1
11.7
7.9
6.2
5.6
Santa Anna Island * Lighthouse
Tutoya* Entrance
Paranahiba River Amarfao Village
Ceara* Lighthouse .
5 25
5 50
11 37
12 00
8.2
8.0
3.9
3.8
Jaguaribe River: Pilot station
Caicara: Village
Cape St Roque: Extreme
4 05
10 17
8.8
4.2
Rio Grande do Norte* Lighthouse
Natal* Cathedral
Parahiba River: Lighthouse at entrance..
Parahiba* Cathedral
Olinda: Lighthouse.
Pernambuco: Picao lighthouse
4 33
10 50
7.0
3.3
Cape St Augustine: Lighthouse
Tamandare* Village
Maceio Lighthouse
4 20
4 17
10 32
10 29
8.5
7.8
4.1
3.7
San Francisco River: Lighthouse at en
trance
Cotinguiba River : Lighthouse at entrance .
Vaza Barris River: Semaphore at en
trance
Real River* Lighthouse
Conde* Village
Garcia d Avila* Tower
Bahia* Santo Antonio lighthouse
4 10
10 22
7.6
3.6
Itaparica: FortonN.pt
Morro de Sao Paulo: Lighthouse
3 50
3 50
10 00
10 00
6.0
6.3
2.9
3.0
Camamu : Village
Contas * Church
APPENDIX IV. [Page 297
MARITIME POSITIONS AND TIDAL DATA.
NORTH AND EAST COASTS OF SOUTH AMERICA Continued.
*j
Place.
Lat. S.
Long.W.
Lun. Int.
Range.
H. W.
L.W.
Spg.
Neap.
j
Ilheoe : Church
h. m.
3 35
ft. TO.
9 47
t<
ft
14 47 40
14 56 40
15 13 27
15 21 00
16 17 20
16 25 38
17 21 40
17 31 45
17 43 30
17 57 31
18 06 15
20 19 23
20 38 25
20 49 00
20 57 35
21 38 40
22 02 00
22 23 45
22 26 00
22 37 00
22 46 00
23 00 42
22 53 15
23 01 43
22 54 46
22 54 24
23 03 40
22 32 00
23 03 40
23 04 20
22 57 20
23 09 20
23 00 30
23 09 50
23 12 20
23 25 55
23 32 57
23 45 15
23 58 30
23 47 20
24 03 06
23 56 00
24 06 30
24 10 32
24 28 45
24 42 35
25 06 40
25 30 55
25 31 20
25 26 30
25 44 10
25 50 15
26 14 17
26 46 45
27 01 35
27 18 00
27 25 30
27 22 55
27 50 27
27 36 00
27 56 40
28 38 00
29 20 20
32 06 40
39 03 25
39 01 45
39 01 15
39 16 45
39 02 05
39 04 15
39 13 15
39 12 00
39 14 36
38 41 46
39 31 16
40 16 36
40 23 46
40 40 45
40 46 35
41 02 21
40 59 00
41 47 35
41 43 15
41 59 45
41 54 05
42 00 00
42 01 15
42 54 05
43 09 19
43 10 21
43 08 45
43 11 01
43 33 24
43 59 26
44 02 29
44 08 24
44 19 04
44 05 45
44 42 04
45 04 04
45 03 50
45 00 39
45 15 20
45 21 04
46 15 57
46 19 09
45 40 49
46 47 44
46 41 04
47 32 54
47 51 50
48 19 53
48 31 03
48 43 14
48 23 14
48 25 51
48 39 29
48 36 59
48 36 44
48 22 20
48 34 25
48 26 09
48 35 16
48 34 14
48 33 44
48 49 45
49 43 39
52 07 44
Olivenca* Center of village
Una* Center of village
Comandatuba * Center of village
Santa Cruz : Church
3 25
9 37
6.0
2.9
Porto Seguro* Matriz Church
Prado River entrance
Alcobaca* Center of village .
Caravellas Center of village
3 10
3 15
9 23
9 27
6.4
7.5
3.1
3.6
Abrolhos Island* Lighthouse
Porto Alere Center of village
E^piritu Santo Bay Lighthouse
2 50
9 00
4.0
1.9
Guarapiri Islets E islet
Benevente: Village
2 40
8 52
5.0
2.4
Itapemirim: Moscas Islet
Sao Joao da Barra: Lighthouse
Cape St Thome* Extreme
Macah* Fort at entrance
2 20
8 30
9.2
4.4
Sant^. Anna TslfVnH Summit
Barra Sao Joao * Village
Busios: Church....
Cape Frio : Lighthouse
Port Frio* Village
2 30
8 42
4.9
2.3
Maricas Islands* S islet
Rio de Janeiro: Fort Villegagnon Light. .
National Observatory
Raza Island* Lighthouse
2 50
9 00
4.2
2.0
Petropolis* Center of town
Cape Guaratiba* Summit
MaVambaya Island: Summit of SW. end..
Mangaratiba : Village
Palmas Bay: Beach at head of bay
Angra dos Reis* Landing place
Ilha Grande* Lighthouse
Parati* Fort
1 35
7 47
5.3
2.5
Ubatuba: Cathedral ....
Porcos Grande Islet: Summit
Busiofl Tslpts* Siirnrriit
St Sebastian Island* Boi Pt li^ht
Villa Nova da Princessa* Center
Santos: Moela I lighthouse. .
Quay
2 50
9 00
5.6
2.8
Alcatrazes Island* Summit 880 ft
Conceica 
