In the ill.u.s.tration (Bowditch p. 88) the earth is supposed to be projected upon the celestial sphere N E S W. The Zenith of the observer is projected at Z and the pole of the earth which is above the horizon is projected at P. The other pole is not given.

The Celestial Equator is marked here E Q W and like all other points and lines previously mentioned, it is the projection of the Equator until it intersects the celestial sphere. Another name for the Celestial Equator is the Equinoctial.

All celestial meridians of longitude corresponding to longitude meridians on the earth are perpendicular to the equinoctial and likewise P S, the meridian of the observer, since it pa.s.ses through the observer's zenith at Z, is formed by the extension of the earth's meridian of the observer and hence intersects the horizon at its N and S points. This makes clear again just what is the meridian of the observer. It is the meridian of longitude which pa.s.ses through the N and S poles and the observer's zenith. In other words, when the sun or any other heavenly body is on your meridian, a line stretched due N and S, intersecting the N and S poles, will pa.s.s through your zenith and the center of the sun or other celestial body. To understand this is important, for no sight with the s.e.xtant is of value except with relation to your meridian.

The Declination of any point in the celestial sphere is its distance in arc, North or South of the celestial equator, i.e., N or S of the Equinoctial.

North declinations, i.e., declinations north of the equinoctial are always marked, +; those south of the equinoctial, -. For instance, in the Nautical Almanac, you will never see a declination of the sun or other celestial body marked, N 18 28' 30". It will always be marked +18 28' 30" and a south declination will be marked -18 28' 30".

Another fact to remember is that Declination on the celestial sphere corresponds to lat.i.tude on the earth. If, for instance, the Sun's declination is +18 28' 30" at noon, Greenwich, then at that instant, i.e., noon at Greenwich, the sun will be directly overhead a point on earth which is in lat.i.tude N 18 28' 30".

The Polar Distance of any point is its distance in arc from either pole.

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 the opposite name.

P M is the polar distance of M from P, or P B the polar distance of B from P.

The true alt.i.tude of a celestial body is its angular height from the true horizon.

The zenith distance of any point or celestial body is its angular distance from the zenith of the observer.

The Ecliptic is the great circle representing the path in which the sun appears to move in the celestial sphere. As a matter of fact, you know that the earth moves around the sun, but as you observe the sun from some spot on the earth, it appears to move around the earth. This apparent track is called the Ecliptic as stated before, and in the ill.u.s.tration the Ecliptic is represented by the curved line, C V T. The plane of the Ecliptic is inclined to that of the Equinoctial at an angle of 23 27-1/2', and this inclination is called the obliquity of the Ecliptic.

The Equinoxes are those points at which the Ecliptic and Equinoctial intersect, and when the sun occupies either of these two positions, the days and nights are of equal length. The Vernal Equinox is that one which the sun pa.s.ses through or intersects in going from S to N declination, and the Autumnal Equinox that which it pa.s.ses through or intersects in going from N to S declination. The Vernal Equinox (V in the ill.u.s.tration) is also designated as the First Point of Aries which is of use in reckoning star time and will be mentioned in more detail later.

The Solst.i.tial 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 the Summer and Winter Solstice according to the season in which the sun appears to pa.s.s these points in its path.

To sum up: The way to find any point on the earth is to find the distance of this point N or S of the equator (i.e., its Lat.i.tude) and its distance E or W of the meridian at Greenwich (i.e., its longitude).

In the celestial sphere, the way to find the location of a point or celestial body such as the sun is to find its declination (i.e., distance in arc N or S of the equator) and its hour angle. By hour angle, I mean the distance in time from your meridian to the meridian of the point or celestial body in question.

a.s.sign for Night reading, Arts, in Bowditch: 270-271-272-273-274-275-277-278-279-280-282-283-284.

WEDNESDAY LECTURE

TIME BY THE SUN--MEAN TIME, SOLAR TIME, CONVERSION, ETC.

There is nothing more important in all Navigation than the subject of Time. Every calculation for determining the position of your ship at sea must take into consideration some kind of time. Put in your Note-Book:

There are three kinds of time:

1. Apparent or solar time, i.e., time by the sun.

2. Mean Time, i.e., clock time.

3. Sidereal Time, or time by the stars.

So far as this lecture is concerned, we will omit any mention of sidereal time, i.e., time by the stars. We will devote this morning to sun time, i.e., apparent time, and mean time.

Apparent or Solar Time is, as stated before, nothing more than sun time or time by the sun. The hour angle of the center of the sun is the measure of apparent or solar time. An apparent or solar day is the interval of time it takes for the earth to revolve completely around on its axis every 24 hours. It is apparent noon at the place where you are when the center of the sun is directly on your meridian, i.e., on the meridian of longitude which runs through the North and South poles and also intersects your zenith. This is the most natural and the most accurate measure of time for the navigator at sea and the unit of time adopted by the mariner is the apparent solar day. Apparent noon is the time when the lat.i.tude of your position can be most easily and most exactly determined and on the lat.i.tude by observation just secured we can get data which will be of great value to us for longitude sights taken later in the day.

Now it would be very easy for the mariner if he could measure apparent time directly so that his clock or other instrument would always tell him just what the sun time was. It is impossible, however, to do this because the earth does not revolve at a uniform rate of speed.

Consequently the sun is sometimes a little ahead and sometimes a little behind any average time. You cannot manufacture a clock which will run that way because the hours of a clock must be all of exactly the same length and it must make noon at precisely 12 o'clock every day. Hence we distinguish clock time from sun time by calling clock time, mean (or average) time and sun time, apparent or solar time. From this explanation you are ready to understand such expressions as Local Mean Time, which, in untechnical language, signifies clock time at the place where you are; Greenwich Mean Time which signifies clock time at Greenwich; Local Apparent Time, which signifies sun time at the place where you are; Greenwich Apparent Time, which signifies sun time at Greenwich.

Now the difference between apparent time and mean time can be found for any minute of the day by reference to the Nautical Almanac which we will take up later in more detail. This difference is called the Equation of Time.

There is one more fact to remember in regard to apparent and mean time.

It is the relation of the sun's hour angle to apparent time. In the first place, what is a definition of the sun's HA? It is the angle at the celestial pole between the meridian intersecting any given point and the meridian intersecting the center of the sun. It is measured by the arc of the celestial equator intersected between the meridian of any point and the meridian intersecting the center of the sun.

[Ill.u.s.tration]

For instance, in the above diagram, suppose PG is the meridian at Greenwich, and PS the meridian intersecting the sun. Then the angle at the pole GPS, measured by the arc GS would be the Hour Angle of Greenwich, or the Greenwich Hour Angle. And now you notice that this angular measure is exactly the same as apparent time at Greenwich or Greenwich Apparent Time, for Greenwich Apparent Time is nothing more than the distance in time Greenwich, England, or the meridian at Greenwich is from the sun, i.e., the time it takes the earth to revolve from Greenwich to the sun; and that distance is exactly measured by the Greenwich Hour Angle or the arc on the celestial equator, GS.

The same is correspondingly true of Local Apparent Time and the ship's Hour Angle. Suppose, for instance, PL is the meridian intersecting the place where your ship is. Then your ship's hour angle would be the angle at the pole intersecting the meridian of your ship and the meridian of the sun or LPS and measured by the arc LS. And you will note that this distance is exactly the same as apparent time at the ship, for Apparent Time at ship is nothing more than the distance in time which the ship is from the sun. We can sum up all this information in a few simple rules, which put in your Note-Book:

Mean Time = Clock Time.

G.M.T. = Greenwich Mean Time.

L.M.T. = Local Mean Time.

Apparent Time = Actual or Sun Time.

G.A.T. (G.H.A.) = Greenwich Apparent Time or Greenwich Hour Angle.

L.A.T. (S.H.A.) = Local Apparent Time or Ship's Hour Angle.

Difference between apparent and mean time or mean and apparent time--Equation of Time.

Right under this in your Note-Book put the following diagram, which I will explain:

[Ill.u.s.tration]

You will see from this diagram that civil time commences at midnight and runs through 12 hours to noon. It then commences again and runs through 12 hours to midnight. The Civil Day, then, is from midnight to midnight, divided into two periods of 12 hours each.

The astronomical day commences at noon of the civil day of the same date. It comprises 24 hours, reckoned from O to 24, from noon of one day to noon of the next. Astronomical time, either apparent or mean, is the hour angle of the true or mean sun respectively, measured to the westward throughout its entire daily circuit.

Since the civil day begins 12 hours before the astronomical day and ends 12 hours before it, A.M. of a new civil day is P.M. of the astronomical day preceding. For instance, 6 hours A.M., April 15th civil time is equivalent to 18 hours April 14th, astronomical time.

Now, all astronomical calculations in which time is a necessary fact to be known, must be expressed in astronomical time. As chronometers have their face marked only from 0 to 12 as in the case of an ordinary watch, it is necessary to transpose this watch or chronometer time into astronomical time. No transposing is necessary if the time is P.M., as you can see from the diagram that both civil and astronomical times up to 12 P.M. are the same. But in A.M. time, such transposing is necessary. Put in your Note-Book:

Whenever local or chronometer time is A.M., deduct 12 hours from such time to get the correct astronomical time:

CT 15d-- 9h--10m--30s A.M.

--12 ------------------------ CT 14d--21h--10m--30s ------

L.M.T. 10d-- 4h--40m--16s A.M.