The last fact to know at this time about the Almanac is found on pages 94-95. Here is given a list of the brighter stars with their positions respectively in the heavens, i.e., their celestial longitude or R.A. on page 94 and their celestial lat.i.tude or declination on page 95. These stars have very little apparent motion. They are practically fixed.

Hence, their position in the heavens is almost the same from January to December though, of course, their position with relation to you is constantly changing, since you on the earth are constantly moving.

The relationship between these various kinds of time is clearly expressed by the following diagram, which put in your Note Book:

[Ill.u.s.tration: Going with arrow, add. Going against arrow, subtract.]

a.s.sign for reading in Bowditch, Articles 294-295-296-297-299-300-301-302-303-304-305-306-307.

If any time is left, have the cla.s.s work out such examples as these:

1. G.M.T. June 20th, 1919, 5h--14m--39s. In Lo. 68 49' W. Required L.S.T., G.S.T., L.M.T., L.A.T.

2. L.M.T. Oct. 15th, 1919, 6h--30m--20s A.M. In Lo. 49 35' 16" E.

Required L.S.T.

3. L.M.T. May 14th, 1919, 10h--15m.--20s A.M. Lo. 56 21' 39" W.

Required L.A.T.

4. W.T. April 20th, 1919, 11h--30m--14s C-W 2h--14m--59s CC 4m--30s slow. In Lo. 89 48' 30" W. Required G.M.T., G.A.T., L.M.T., L.A.T., G.S.T., L.S.T.

5. What is Declination and R.A. on May 15th, 1919, of Polaris, Arcturus, Capella, Regulus, Altair, Deneb, Vega, Aldebaran?

6. What is the sun's declination and R.A., Time at Greenwich, July 30th:

7h--14m--39s A.M.

4h--29m--14s A.M.

3h--04m--06s 11h--49m--59s 2h--14m--30s A.M.?

SAt.u.r.dAY LECTURE

CORRECTION OF OBSERVED ALt.i.tUDES

The true alt.i.tude of a heavenly body is the angular distance of its center as measured from the center of the earth. The observed alt.i.tude of a heavenly body as seen at sea by the s.e.xtant may be converted to the true alt.i.tude by the application of the following four corrections: Dip, Refraction, Parallax and Semi-diameter.

Dip of the horizon means an increase in the alt.i.tude caused by the elevation of the eye above the level of the sea. The following diagram ill.u.s.trates this clearly:

[Ill.u.s.tration]

If the eye is on the level of the sea at A, it is in the plane of the horizon CD, and the angles EAC and EAD are right angles or 90 each. If the eye is elevated above A, say to B, it is plain that the angles EBC and EBD are greater than right angles, or in other words, that the observer sees more than a semi-circle of sky. Hence all measurements made by the s.e.xtant are too large. In other words, the elevation of the eye makes the angle too great and therefore the correction for dip is always subtracted.

Refraction is a curving of the rays of light caused by their entering the earth's atmosphere, which is a denser medium than the very light ether of the outer sky. The effect of refraction is seen when an oar is thrust into the water and looks as if it were bent. Refraction always causes a celestial object to appear higher than it really is. This refraction is greatest at the horizon and diminishes toward the zenith, where it disappears. Table 20A in Bowditch gives the correction for mean refraction. It is always subtracted from the alt.i.tude. In the higher alt.i.tudes, select the correction for the nearest degree.

You should avoid taking low alt.i.tudes (15 or less) when the atmosphere is not perfectly clear. Haziness increases refraction.

Parallax is simply the difference in angular alt.i.tude of a heavenly body as measured from the center of the earth and as measured from the corresponding point on the surface of the earth. Parallax is greatest when the body is in the horizon, and disappears when it is at the zenith.

[Ill.u.s.tration]

When the angular alt.i.tude of the sun in this diagram is 0, the parallax ABC is greatest. When the alt.i.tude is highest there is no parallax. The sun is so far away that its parallax never exceeds 9". The stars have practically none at all from the earth's surface. Parallax is always to be added in the case of the sun.

The semi-diameter 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 SD varies with the distance. Thus, the difference of the sun's SD at different times of the year is due to the change of the earth's distance from the sun.

[Ill.u.s.tration]

The SD is to be added to the observed alt.i.tude in case the lower limb is brought in contact with the horizon, and subtracted if the upper limb is used. Probably most of the sights you take will be of the sun's lower limb, i.e., when the lower limb is brought in contact with the horizon, so all you need to remember is that in that event the SD is additive.

Now at first we will correct alt.i.tudes by applying each correction separately, but as soon as you get the idea, there is a short way to apply all four corrections at once. This is done in Table 46. However, disregard that for the moment. Put this in your Note-Book:

Dip is -. Table 14 Bowditch Refraction is -. " 20 A Bowditch Parallax is +. " 16 Bowditch S.D. is +. Nautical Almanac

Observed alt.i.tude of Sun's lower limb is expressed (_).

True alt.i.tude is expressed -(-)-.

Remember that before an observation is at all accurate, it must be corrected to make it a true alt.i.tude. Remember also that the IE must be applied, in addition to these other corrections, in order to make the observed alt.i.tude a -(-)- alt.i.tude. So there are really five corrections to make instead of four, providing, of course, your s.e.xtant has an IE.

Examples:

1. June 20th, 1919, observed alt.i.tude of (_) 69 25' 30". IE + 2' 30".

HE 16 ft. Required -(-)-.

2. April 15th, 1919, observed alt.i.tude of (_) 58 29' 40". IE - 2' 30".

HE 18 ft. Required -(-)-.

3. March 4th, 1919, observed alt.i.tude of (_) 44 44' 10". IE - 4' 20".

HE 20 ft. Required -(-)-.

Etc.

WEEK IV--NAVIGATION

TUESDAY LECTURE

THE LINE OF POSITION

It is practically impossible to fix your position exactly by one observation of any celestial body. The most you can expect from one sight is to fix your line of position, i.e., the line somewhere along which you are. If, for instance, you can get a sight by s.e.xtant of the sun, you may be able to work out from this sight a very accurate calculation of what your lat.i.tude is. Say it is 50 N. You are practically certain, then, that you are somewhere in lat.i.tude 50 N, but just where you are you cannot tell until you get another sight for your longitude. Similarly, you may be able to fix your longitude, but not be able to fix your lat.i.tude until another sight is made. Celestial Navigation, then, reduces itself to securing lines of position and by manipulating these lines of position in a way to be described later, so that they intersect. If, for instance, you know you are on one line running North and South and on another line running East and West, the only spot where you _can_ be on _both_ lines is where they intersect.

This diagram will make that clear: