Azimuths and Amplitudes
Of all the navigational instruments now in practical use, there are
few, if any, that exceed the mariner’s compass in usefulness to
mankind. The part it has played in the development of the world has
been most important, and its utility is no less to-day than in the
past, for the intercourse of nations is still guided by the compass
needle. With such a responsibility depending on this instrument, it
would naturally be supposed that its indications must be very accurate,
but, on the contrary, the needle is swayed by the slightest magnetic
influence and points North only on rare occasions; and in steel vessels
only by mere chance.
The needle is drawn from true north first by the direction of the
earth’s magnetic force which is not coincident with the meridian owing
to the position of the magnetic poles. The north magnetic pole being
in the extreme northern part of Canada, all the lines of force in the
northern hemisphere converge toward this locality. The needle when
otherwise undisturbed lies in the direction of these lines of force and
takes an angle with the meridian depending on the locality.
The amount of divergence from the true north, or variation, as it is
called, differs in different localities but is readily obtained by
a glance at the chart where each compass rose shows the amount of
variation at that place. From a magnetic course, or bearing, the true
course, or bearing, is readily found by the proper application of
this variation, which may be either easterly or westerly. The _true_
course is to the _right_ of the magnetic course, when considered
from the center of the compass, in _easterly_ variation; T. R.
E.--True-Right-Easterly. Remember these three words and the whole
lesson is learned, for if true is to the right in easterly variation
it must be to the left in westerly; and if true is to the right in
easterly, the magnetic course must be to the left of true course
in easterly and to the right in westerly. In this way the true and
magnetic courses are converted one to the other at will.
If we were to sail always in an entirely wooden ship, our compass
troubles would be very few, for the above would include every
phase of the situation. As wood is non-magnetic the compass would
be uninfluenced by outside disturbances. Wood, as a ship-building
material, having been so much displaced by iron and steel, the use of
these metals has brought many problems to solve in connection with the
deflection of the compass needle.
The effect on the compass needle of the magnetism in a vessel and her
cargo is known as deviation and is very complicated, owing to many
influences which are at work at all times giving an ever-varying value
to this element of error.
The causes of deviation and its treatment in the way of compensating
the compass are subjects much too extensive for this little book;
furthermore, they are carefully dealt with in a half dozen of the
well-known works on navigation, so we will touch only on the every-day
side of compass work.
The deviation changes with every alteration of the vessel’s head, owing
to the change in position of prominent parts of the vessel’s hull
relative to each other, to the compass, and to the terrestrial lines of
force (magnetism).
As a result of these influences on the compass needle, the mariner
has three courses to deal with. The first is the true course, which
is based on a compass whose needle points true north. The second, the
magnetic course, is taken from a compass affected by variation alone
and therefore pointing to the magnetic pole. The third is the compass
course, or that course actually shown by an ordinary standard compass
in a steel ship, affected by the error of variation combined with the
error of deviation.
The combination of the deviation and the variation is the compass
error and is obtained by adding the deviation and variation if both
are of the same name, the compass error taking that name; for instance
suppose we have a variation of 2° W. and deviation of 10° W., the
combined error is 12° W. If, however, the variation and deviation are
of different names, it becomes necessary to find the difference between
the two and name the result after the greater quantity; thus, with a
deviation of 4° E. and a variation of 10° W., the error is 6° W.
The compass error is applied to compass course to obtain true course
and vice versa by the same rule as for variation.
The navigator in planning his course between two positions lays the
parallel rulers on these positions on the chart and carries this
direction to the nearest compass rose. This may be a true rose, in
which event he remembers his T. R. E. rule, reversing it in this
case, and with the variation given on the chart secures the magnetic
course. In an iron or steel vessel, the deviation for that course
must be ascertained from the deviation card by trial or from a Napier
Diagram direct and applied to the magnetic course in order to obtain
the compass course. This is accomplished precisely as in finding the
magnetic from the true course (to the left if deviation is easterly and
to the right if westerly). The course by standard compass is now at
hand by which we can steam from one selected point to the other.
The deviation as has been said is an ever-varying error, and
consequently it is quite impracticable to depend wholly on a fixed
deviation card. We may take aboard some magnetic cargo or change our
latitude to a great extent, the vessel may be pounded excessively by
heavy seas, a stroke of lightning or by stranding; all these are causes
liable to affect the deviation more or less.
In order to forestall the serious consequences that are liable to
attend such a derangement of the normal and expected deviation, the
careful navigator takes azimuths or amplitudes on every course when
practicable. Azimuths and amplitudes are nothing more nor less than
astronomical bearings of heavenly bodies; they indicate the true
bearing of the body, and the difference between this bearing and the
bearing taken simultaneously by standard compass is the compass error.
The azimuth of a body is the angle at the zenith between the meridian
and the vertical circle passing through the body. It is customary,
however, to consider the azimuth as measured by the arc of the horizon
rather than by the angle at the zenith. It is measured from the north
or south point according to the latitude, toward either the east or
west point, through 180°.
An amplitude, unlike an azimuth, is restricted as to time of
observation, for the body must be on the horizon either rising or
setting; and should be observed when the sun is about its own diameter
above the horizon and with a not excessive height of eye. The amplitude
is measured from the east or west point through 90° to the north or
south point. If the body observed has a south declination and is
rising, the amplitude will be East so much South; if declination is
north, East so much North, for a body rises in the East point when its
declination is 0°--on the equator.
The principle of the amplitude lies in the solution of a right-angled
spherical triangle, whose sides are the body’s polar distance, the
co-latitude, and the zenith distance which is 90°. We desire the
complement of the angle at the zenith. It is unnecessary to compute
an amplitude, for in Table 39, Bowditch, will be found the desired
bearings for different latitudes and declinations. The sun will be
found the most satisfactory of the heavenly bodies to utilize for
amplitudes.
There are two methods of calculating an azimuth, one known as the time
azimuth and the other as the altitude azimuth. The former is the most
popular owing to the tables that have been compiled, an inspection of
which facilitates the navigator in quickly obtaining the true azimuth
of a body. Before entering the tables, it is necessary to have as
arguments the latitude and declination, and, if using the sun, the
local apparent time, or for stellar work the hour angle. Should the
star’s hour angle exceed 12 hours, 12 hours should be subtracted from
it, and the remainder used as P.M. time. A planet may be employed
precisely in the same manner as a star.
One of the simplest and most expeditious methods of securing the
azimuth is by means of a diagram. Upon this convenient invention
the bearing of a body can very quickly be taken off with a pair of
rulers. Weir’s Azimuth Diagram is sold by the Hydrographic Office for
a very small sum. The only argument that can be used against its use
is that it requires a small table to lay it upon. Simple and complete
directions are printed on the diagram.
The altitude azimuth is often computed at the same time as the ordinary
A.M. and P.M. time sights, utilizing the altitude of the body for
both operations. The principle involved in computing both an altitude
azimuth and a time azimuth is the solution of the same astronomical
triangle for the same angle, but in the case of the altitude azimuth
three sides are given (the co-latitude, the zenith distance, and polar
distance) to find the angle at the zenith. In the time azimuth, two
sides and the included angle are given (the polar distance, co-latitude
and local apparent time or hour angle) to find also, the angle at the
zenith.
The azimuth found by computation should be named North if in north
latitude, or South if in south latitude.
It has been customary to add up the logs, divide by 2 and the cosine
will be half the azimuth named from the elevated pole, but a more
expeditious way is after adding the logs seek in the log haversines
and find the azimuth directly but named from the opposite pole to the
latitude. With the correct bearing of the sun, and its simultaneous
bearing by standard compass at hand, the compass error is found by
merely taking their difference. Now this error, as said before, is
composed of the sum or difference of the deviation and the variation,
so, if either is subtracted from their sum, or added to their
difference the remainder is the other quantity. The variation being
always known is subtracted from or added to the compass error to obtain
the deviation, thus checking the deviation card for that particular
course the vessel was steering at the time of observation.
With the compass error at hand, many students become perplexed as to
the proper manner of dealing with this error, and finding from it the
deviation. The compass error is first named, by considering the two
bearings (compass and true) from the center of the compass; if the true
is to the right of the compass bearing, the error is easterly, if to
the left, westerly.
Now should the variation happen to be identical with the compass error,
both in amount and in name, there is no deviation; if the variation is
0°, then the whole error is deviation. If by chance the compass error
is 0°, it indicates that the variation and deviation are equal in
amount and opposed to each other in their influence on the needle. The
deviation, in such a case, naturally takes the opposite name from the
variation.
In separating the variation from the compass error, it is necessary to
exercise a little thought and to consider what deviation applied to the
given variation will produce that compass error. This will be readily
seen after a little practice. There are, however, some rules which are
here given, by which the deviation can be obtained mechanically.
The deviation is the difference between the variation and the compass
error if they are of the same name or adding them if of different
names. It is given the same name as the compass error unless the
compass error is subtracted from the variation, when the deviation
takes the opposite name.
Or a diagram in which the error is shown by its particular number
of degrees east or west of the true north line may be drawn and the
variation likewise properly shown east or west of true north. If the
error is to the left of the variation the deviation is west and if to
the right the deviation is east.