  We have already discussed the way in which the earth is divided so as to aid us in finding our position at sea, i.e., with an equator, parallels of latitude, meridians of longitude starting at the Greenwich meridian, etc. We now take up the way in which the celestial sphere is correspondingly divided and also simple explanations of some of the more important terms used in Celestial Navigation. As you stand on any point of the earth and look up, the heavenly bodies appear as though they were situated upon the surface of a vast hollow sphere, of which your eye is the center. Of course this apparent concave vault has no existence and we cannot accurately measure the distance of the heavenly bodies from us or from each other. We can, however, measure the direction of some of these bodies and that information is of tremendous value to us in helping us to fix our position. Now we could use our eye as the center of the celestial sphere but more accurate than that is to use the center of the earth. Suppose we do use the center of the earth as the place from which to observe these celestial bodies and, in imagination, transfer our eye there. Then we will find projected on the celestial sphere not only the heavenly bodies but the imaginary points and circles of the earth's surface. Parallels of latitude, meridians of longitude, the equator, etc., will have the same imaginary position on the celestial sphere that they have on the earth. Your actual position on the earth will be projected in a point called your zenith, i.e., the point directly overhead. The Celestial Sphere From this we get the definition that the Zenith of an observer on the earth's surface is the point in the celestial sphere directly overhead. It would be a simple matter to fix your position if your position never changed. But it is always changing with relation to these celestial bodies. First, the earth Now with these facts in mind, let us explain in simple words the meaning of some of the terms you will have to become acquainted with in Celestial Navigation. In the illustration (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 passes 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 passes 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 pass through your zenith and the center of the sun or other celestial body. To understand this is important, for no sight with the sextant 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 latitude 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 latitude N 18° 28' 30". The Polar Distance of any point is its distance in arc from either pole. It P M is the polar distance of M from P, or P B the polar distance of B from P. The true altitude 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 illustration 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° 27½', 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 passes through or intersects in going from S to N declination, and the Autumnal Equinox that which it passes through or intersects in going from N to S declination. The Vernal Equinox (V in the illustration) 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 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 the Summer and Winter Solstice according to the season in which the sun appears to pass 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 Latitude) 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. Assign for Night reading, Arts, in Bowditch: 270-271-272-273-274-275-277-278-279-280-282-283-284. 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 latitude of your position can be most easily and most exactly determined and on the latitude 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. Hour Angle of Greenwich 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: Twelve and Twentyfour Hour Clocks 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:
Now we come to a very important application of time. You will remember that in one of the former lectures we stated that to find our latitude, we had to find how far North or South of the equator we were, and to find our longitude, we had to find how far East or West of the meridian at Greenwich we were. Never mind about latitude for the present. We can find our longitude exactly if we know our Greenwich time and our time at ship. For instance, in the accompanying diagram: East and West Longitude Suppose PG is the meridian at Greenwich, then anything to the west of PG is West longitude and anything to the East of PG is East longitude. Now suppose GPS is the H.A. of G. or G.A.T. - i.e., the distance in time G. is from the sun. And L P S is the H.A. of the ship or L.A.T. - i.e., the distance in time the ship is from the sun. Then the difference between G P S and L P S is G P L, measured by the arc L G, and that is the difference that the ship, represented by its meridian PL, is from the Greenwich meridian PG. In other words, that is the ship's longitude for, as mentioned before, longitude is the distance East or West of Greenwich that any point is, measured on the arc of the celestial equator. The longitude is West, for you can see LPG or the arc LG is west of the meridian PG. Likewise if P E is the meridian of your ship, the Longitude in time is the S.H.A. or L.A.T., E P S (the distance your ship is from the sun) less the G.H.A. or G.A.T., G P S (the distance Greenwich is from the sun) which is the angle G P E measured by the arc G E. And this Longitude is East for you can see G P E, measured by G E, is east of the Greenwich meridian, P G. In both these cases, however, the longitude is expressed in time, i.e., so many hours, minutes and seconds from the Greenwich meridian and we wish to express this distance in degrees, minutes and seconds of arc. The earth describes a circle of 360° every 24 hours. Then if you are 1 hour from Greenwich, you are 1/24 of 360° or 15° from Greenwich and if you are 12 hours from Greenwich, you are ½ of 360° or 180° from Greenwich. By keeping this in mind, you should be able to transpose time into degrees, minutes and seconds of arc for any fraction of time. It is, however, all worked out in Table 7 of Bowditch which turn to. (Note to Instructor: Explain this table carefully). Put in your Note-Book: 89° 24' 26" = (89°) 5h 56m Also put in your Note-Book this diagram and these formulas: (For diagram use illustration on p. 40.)
If G.M.T. or G.A.T. is greater than L.M.T. or L.A.T. respectively, Lo. is West. If G.M.T. or G.A.T. is less than L.M.T. or L.A.T. respectively, Lo. is East. Example: In longitude 81° 15' W, L.M.T. is April 15d 10h 17m 30s A.M. What is G.M.T.? L.M.T. 15d 10h 17m 30s A.M. G.M.T. April 15d 3h 42m 30s L.M.T. April 15d 10h 17m 30s A.M. In what Lo. is ship? G.M.T. 15d 3h 42m 30s L.M.T. 14d 22h 17m 30s Lo. = 81° 15'W Assign also for Night Work reading the following articles in Bowditch: 276-278-279-226-228-286-287-288-290-291-294 (omitting everything on page 114.)
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| L.M.T. | 10h 40m 30s |
| Lo. in T | 4 56 W + |
| —————— | |
| G.M.T. | 15 36 30 |
| Circle enclosing dot.R.A. | 5 11 10 |
| Circle enclosing a Cross.C.P. | 2 34 |
| —————— | |
| G.S.T. | 20 50 14 |
| Lo. W | -4 56 |
| —————— | |
| L.S.T. | 15h 54m 14s |
Now Bowditch gets this L.S.T. in still another way. Turn to page 110, Article 290. There the formula used is L.M.T. + Circle enclosing dot.R.A. + Circle enclosing a Cross.C.P. = L.S.T, and in order to get the correct Circle enclosing dot.R.A. and Circle enclosing a Cross.C.P. the G.M.T. has to be secured by the formula L.M.T. + W.Lo. = G.M.T.
- E.Lo.
Let us work this same example in Bowditch by the other two methods. First by the formula
L.M.T. + W.Lo. = G.M.T. + Circle enclosing dot.R.A. + Circle enclosing a Cross.C.P.= G.S.T. - W.Lo. = L.S.T.
- E.Lo.+ E.Lo.
L.M.T. 22d 2h 00m 00s
+ W. Lo. 5 25
————————
G.M.T. 22d 7h 25m 00s
Circle enclosing dot.R.A. 1 57 59
Circle enclosing a Cross.C.P. 1 13
————————
G.S.T. 22d 9h 24m 12s
- W. Lo. 5 25
————————
L.S.T. 22d 3h 59m 12s
The small difference between this answer and that of Bowditch's is that the Circle enclosing dot.R.A. for 1916 is slightly different from that of 1919. Bowditch used the 1916 Almanac, whereas we are working from the 1919 Almanac. Now turn to page 107 of the N.A. and let us work the same example in Bowditch by the method used here:
| L.M.T. | 2h - 00m - 00s |
| Red. for 2h | 0 - 20 |
| Circle enclosing dot.R.A. 0h | 1 - 57 - 59 |
| Red. Lo. 5h - 25m | 0 - 53 |
| ——————— | |
| L.S.T. | 3h - 59m - 12s |
The reason I am going so much into detail in explaining methods of finding L.S.T. is because, by a very simple calculation which will be explained later, we can get our latitude at night if we know the altitude of Polaris (The North Star) and if we know the L.S.T. at the time of observation. Some of you may think that the N.A. way is the simplest. It is given in the N.A., and in an examination it would be permissible for you to use the N.A. as a guide because, in an examination, I propose to let you have at hand the same books you would have in the chart house of a ship. On the other hand, the method given in the N.A. is not as clear to my mind as the method which starts with L.M.T., then finds with the Longitude the G.M.T. That gives you, roughly speaking, the distance in time Greenwich is from the sun. Add to that the sun's R.A. or the distance in time the sun is from the First Point of Aries at Greenwich Mean Noon. Add to that the correction for the time past noon. The result is G.S.T. Now all you have to do is to apply the longitude correctly to find the L.S.T., just as when you have G.M.T. and apply the longitude correctly you get L.M.T. That is a method which does not seem easy to forget, for it depends more upon simple reasoning where the others, for a beginner, depend more upon memory. However, any of the three methods is correct and can be used by you. Perhaps the best way is to work a problem by two of the three that seem easiest. In this way you can check your figures. When I give you a problem that involves finding the L.S.T. I do not care how you get the L.S.T. providing it is correct when you get it.
Assign for Night Reading in Bowditch the following Arts.: 282-283-284-285. Also the following questions:
1. Given the G.M.T. and the longitude in T which is W, what is the formula for L.S.T.?
2. Given the L.A.T. and longitude in T which is E, what is the formula for G.S.T.?
3. Given the L.S.T. and longitude in T which is W. Required G.M.T.
Etc.
The Nautical Almanac
For the last two days we have been discussing Time - sun time or solar time and star time or sidereal time. Now let us examine the Nautical Almanac to see how that time is registered and how we read the various kinds of time for any instant of the day or night. Before starting in, put a large cross on pages 4 and 5. For any calculations you are going to make, these pages are unnecessary and they are liable to lead to confusion.
Sun time of the mean sun at Greenwich is given for every minute of the day in the year 1919 in the pages from 6 to 30. This is indicated by the column to the left headed G.M.T. Turn to page 6 under Wednesday, Jan. 1st. You can see that the even hours are given from 0 to 24. Remember that these are expressed in astronomical time, so that if you had Jan. 2nd - 10 hours A.M., you would not look in the column under Jan. 2nd but under the column for Jan. 1st, 22 hours, since 10 A.M. Jan. 2nd is 22 o'clock Jan. 1st, and no reading is used in this Almanac except a reading expressed in astronomical time. Now at the bottom of the column under Jan. 1st you see the letters H.D. That stands for "hourly difference" and represents the amount to be added or subtracted for an odd hour from the nearest even hour. In this instance it is .2. You note that even hours 2, 4, 6, etc., are given. To find an odd hour during this astronomical day, subtract .2 from the preceding even hour. For any fraction of an hour you simply take the corresponding fraction of the H.D. and subtract it from the preceding even hour. For instance, the declination for Jan. 1st - 12 hours would be 23° 1.8' or 23° 1' 48", 13 hours would be 23° 1.6' or 23°1'36", 12½ hours would be 23° 1.7' or 23°1'42", and 13½ hours would be 23° 1.5' or 23°1'30".
Now to the right of the hours you note there is given the corresponding amount of Declination and the Equation of Time. Before going further, let us review a few facts about Declination. The declination of a celestial body is its angular distance N or S of the celestial equator or equinoctial. Now get clearly in your mind how we measure the angular distance from the celestial equator of any heavenly body. It is measured by the angle one of whose sides is an imaginary line drawn to the center of the earth and the other of whose sides is an imaginary line passing from the center of the earth into the celestial sphere through the center of the heavenly body whose declination you desire. Now as you stand on any part of the earth, you are standing at right angles to the earth itself. Hence if this imaginary line passed through you it would intersect the celestial sphere at your zenith, i.e., the point in the celestial sphere which is directly above you. Now suppose you happen to be standing at a certain point on the earth and suppose that point was in 15° N latitude. And suppose at noon the center of the sun was directly over you, i.e., the center of the sun and your zenith were one and the same point. Then the declination of the sun at that moment would be 15° N. In other words, your angular distance from the earth's equator (which is another way of expressing your latitude) would be precisely the same as the angular distance of the center of the sun from the celestial equator. Suppose you were standing
Put in your Note-Book:
| North Declination is expressed +. |
| South Declination is expressed - . |
Now turn to page 6 of the Nautical Almanac. You will see opposite Jan. 1st 0h, a declination of - 23° 4.2'. Every calculation in this Almanac is based on time at Greenwich, i.e., G.M.T. So at 0h Jan. 1st at Greenwich - that is at noon - the Sun's declination is S 23° 4.2'.
You learned in the lecture the other day on solar time, that the difference between mean time and apparent time was called the equation of time. This equation of time, with the sign showing in which way it is to be applied, is given for any minute of any day in the column marked "Equation of Time." You will also notice that there is an H.D. for equations of time just as there is for each declination, and this H.D. should be used when finding the equation of time for an odd hour.
Put in your Note-Book:
1. The equation of time is to be applied as given in the Nautical Almanac when changing Mean Time into Apparent Time.
2. When changing Apparent Time into Mean Time, reverse the sign as given in the Nautical Almanac.
That is all there is to finding sun time, either mean or apparent, for any instant of any day in the year 1919. Do not forget, however, that all this data is based upon Greenwich Mean Time. To find Local Mean Time you must apply the Longitude you are in. To find Local Apparent Time you must first secure G.A.T. from G.M.T. and then apply the Longitude.
(Note to Instructor: Make the class work out conversions here if you have time to do so and can finish the rest of the lecture by the end of the period.)
So much for time by the sun. Now let us examine time by the stars - sidereal time. Turn to pages 2-3. There you find the Right Ascension of the Mean Sun at Greenwich Mean Noon for every day in the year. You remember that, roughly speaking, the Sun's Right Ascension was the distance in time the sun was from the First Point of Aries. So these tables give that distance (expressed in time) for noon at Greenwich of every day. For the correction to be applied for all time after noon at Greenwich (i.e., Circle enclosing a Cross.C.P.), use the table at the bottom of the page. For instance, the Circle enclosing dot.R.A. at Greenwich 9h 24m on Jan. 1st would be
| Circle enclosing dot.R.A. | 18h 40m 21s |
| Circle enclosing a Cross.C.P. | 1 33 |
| —————— | |
| 18h 41m 54s |
Now we must go back to some of the formulas we learned when discussing star time and apply them with the information we now have from the Nautical Almanac. If the G.M.T. on April 20th is 4h 16m 30s, what is the G.S.T. for the same moment? That is, when Greenwich is 4h 16m 30s from the sun, how far is Greenwich from the First Point of Aries? You remember the formula was G.S.T. = G.M.T. + Circle enclosing dot.R.A. + Circle enclosing a Cross.C.P.
| G.M.T. | 4h 16m 30s |
| Circle enclosing dot.R.A. | 1 50 6 |
| Circle enclosing a Cross.C.P. | 0 42 |
| —————— | |
| G.S.T. | 6h 07m 18s |
Suppose you were in Lo. 74° W. What would be the R.A.M. (L.S.T.)? You remember the formula for L.S.T. from G.S.T. was the same relatively as L.M.T. from G.M.T., i.e., L.S.T. = G.S.T. - W. Lo.
+ E. Lo,
Here it would be
| G.S.T. | 6h 07m 18s |
| (74° W) | - 4 56 00 |
| ——————— | |
| L.S.T. | 1h 11m 18s |
Suppose you are at sea in Lo. 70° W and your CT is October 20th 6h 4m 30s A.M., CC 2m 30s fast. You wish to get the R.A. of your M, i.e., the L.S.T. How would you go about it? The first thing to do would be to get your G.M.T. It is CT—CC.
| 20d 06h 04m 30s A.M. | |
| - 12 | |
| ————————— | |
| CT | 19d 18h 04m 30s |
| CC | - 02 30 |
| ————————— | |
| G.M.T. | 19d 18h 02m 00s |
| Then get your G.S.T. | |
| Oct. | 19d 18h 02m 00s |
| Circle enclosing dot.R.A. | 13 47 38.5 |
| Circle enclosing a Cross.C.P. | 2 57.7 |
| ————————— | |
| 19d 31h 52m 36.2s | |
| - 24 | |
| ————————— | |
| G.S.T. | 19d 7h 52m 36.2s |
| Then get your L.S.T. | |
| G.S.T. | 7h 52m 36.2s |
| W.Lo ( - ) | 4 40 |
| ————————— | |
| L.S.T. | 3h 12m 36.2s |
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 latitude 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:
Relationship between different kinds of time
Assign 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 class work out such examples as these:
1. G.M.T. June 20th, 1919, 5h14m39s. 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, 6h30m20s A.M. In Lo. 49° 35' 16" E. Required L.S.T.
3. L.M.T. May 14th, 1919, 10h15m. 20s A.M. Lo. 56° 21' 39" W. Required L.A.T.
4. W.T. April 20th, 1919, 11h30m14s 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.? |
Correction Of Observed Altitudes
The true altitude of a heavenly body is the angular distance of its center as measured from the center of the earth. The observed altitude of a heavenly body as seen at sea by the sextant may be converted to the true altitude by the application of the following four corrections: Dip, Refraction, Parallax and Semi-diameter.
Dip of the horizon means an increase in the altitude caused by the elevation of the eye above the level of the sea. The following diagram illustrates this clearly:
Illustration of effect of height of eye above sea level
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 sextant 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 altitude. In the higher altitudes, select the correction for the nearest degree.
You should avoid taking low altitudes (15° or less) when the atmosphere is not perfectly clear. Haziness increases refraction.
Parallax is simply the difference in angular altitude 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.
Effect of Parallax
When the angular altitude of the sun in this diagram is 0, the parallax ABC is greatest. When the altitude 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.
Illustration of semi-diameter
The SD is to be added to the observed altitude in case the lower limb is brought in contact with the horizon, and subtracted if the upper limb is used. Probably
Now at first we will correct altitudes 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 -. | Table 20 Bowditch |
| Parallax is +. | Table 16 Bowditch |
| S.D. is +. | Nautical Almanac |
Observed altitude of Sun's lower limb is expressed Circle with line under.
True altitude is expressed Circle with line through.
Remember that before an observation is at all accurate, it must be corrected to make it a true altitude. Remember also that the IE must be applied, in addition to these other corrections, in order to make the observed altitude a Circle with line through altitude. So there are really five corrections to make instead of four, providing, of course, your sextant has an IE.
Examples:
1. June 20th, 1919, observed altitude of Circle with line under 69° 25' 30". IE + 2' 30". HE 16 ft. Required Circle with line through.
2. April 15th, 1919, observed altitude of Circle with line under 58° 29' 40". IE - 2' 30". HE 18 ft. Required Circle with line through.
3. March 4th, 1919, observed altitude of Circle with line under 44° 44' 10". IE - 4' 20". HE 20 ft. Required Circle with line through.
Etc.
