Chapter 7
2. May 15th, 1919. D.R. latitude 19 deg. 20' S, Longitude 40 deg. 15' 44" E. CT 10h--44m--55s A.M. CC 3m--10s fast. Find TZ.
Note to Instructor:
If possible, give more examples to find TZ and also some examples on latitude by meridian altitude.
Assign for Night Work reading the following Articles in Bowditch: 371-372-373-374-375. Also, examples to find TZ.
FRIDAY LECTURE
MARC ST. HILAIRE METHOD BY A SUN SIGHT
You have learned how to get your latitude by an observation at noon. By the Marc St. Hilaire Method, which we are to take up today, you will learn how to get a line of position, at any hour of the day. By having this line of position intersect your parallel of latitude, you will be able to establish the position of your ship, both as to its latitude and longitude.
Now you have already learned that in order to get your latitude accurately, you must wait until the sun is on your meridian, i.e., bears due North or South of you, and then you apply a certain formula to get your latitude. When the sun is on or near the prime vertical (i.e., due East or West) you might apply another set of rules, which you have not yet learned, to get your longitude. By the Marc St. Hilaire method, the same set of rules apply for getting a line of position at any time of the day, no matter what the position of the observed body in the heavens may be. Just one condition is necessary, and this condition is necessary in all calculations of this character, i.e., an accurate measurement of the observed body's altitude is essential.
What we do in working out the Marc St. Hilaire method, is to assume our Dead Reckoning position to be correct. With this D. R. position as a basis, we compute an altitude of the body observed. Now this altitude would be correct if our D. R. position were correct and vice versa. At the same time we measure by sextant the altitude of the celestial body observed, say, the sun. If the computed altitude and the actual observed altitude coincide, the D. R. position is correct. If they do not, the computed altitude must be corrected and the D. R. position corrected to coincide with the observed altitude. Just how this is done will be explained in a moment. Put in your Note-Book:
_Formula for obtaining Line of Position by M. St. H. Method._
I. Three quantities must be known either from observation or from Dead Reckoning.
1. The S. H. A., marked "t."
Note: The method for finding S. H. A. (t) differs when the sun or star is used as follows:
(a) For the Sun: Get G.M.T. from the corrected chronometer time. Apply the equation of time to find the G.A.T. Apply the D.R. Lo. (-W) (+E) and the result is L.A.T. or S.H.A. as required.
(b) For a Star: (Note to pupils: Leave this blank to be filled in when we take up stars in more detail.)
2. The Latitude, marked "L."
3. The Declination of the observed body, marked "D."
II. Add together the log haversine of the S.H.A. (Table 45), the log cosine of the Lat. (Table 44), and the log cosine of the Dec. (Table 44) and call the sum S. S is a log haversine and must always be less than 10. If greater than 10, subtract 10 or 20 to bring it less than 10.
III. With the log haversine S enter table 45 in the adjacent parallel column, take out the corresponding Natural Haversine, which mark N_{S}.
IV. Find the algebraic difference of the Latitude and Declination, and from Table 45 take out the Natural Haversine of this algebraic difference angle. Mark it N_{D+-L}
V. Add the N_{S} to the N_{D+-L}, and the result will be the Natural Haversine of the calculated zenith distance. Formula N_{ZD} = N_{S} + N_{D+-L}
VI. Subtract this calculated zenith distance from 90 deg. to get the calculated altitude.
VII. Find the difference between the calculated altitude and the true altitude and call it the altitude difference.
VIII. In your Azimuth Table, find the azimuth for the proper "t," L and D.
IX. Lay off the altitude difference along the azimuth either away from or toward the body observed, according as to whether the true altitude, observed by sextant, is less or greater than the calculated altitude.
X. Through the point thus reached, draw a line at right angles to the azimuth. This line will be your Line of Position, and the point thus reached, which may be read from the chart or obtained by use of Table 2 from the D. R. Position, is the nearest to the actual position of the observer which you can obtain by the use of any method from one sight only.
Example:
At sea, May 18th, 1919, A.M. (_) 29 deg. 41' 00". D.R. Latitude 41 deg. 30' N, Longitude 33 deg. 38' 45" W. WT 7h 20m 45s A.M. C-W 2h 17m 06s CC + 4m 59s. IE--30". HE 23 ft. Required Line of Position and most probable position of ship.
WT 18d -- 7h -- 20m -- 45s A.M. -- 12 ------------------------ WT 17d -- 19h -- 20m -- 45s C-W 2 -- 17 -- 06 Corr. + 9' 34" ------------------------ IE -- 30 CT 17d -- 21h -- 37m -- 51s ------------ CC + 4 -- 59 + 9' 04" ------------------------ G.M.T. 17d -- 21h -- 42m -- 50s (_) 29 deg. 41' 00" Eq. T. + 3 -- 47 + 9 04 ------------------------ ------------ G.A.T. 17d -- 21h -- 46m -- 37s -(-)- 29 deg. 50' 04" Lo. in T 2 -- 14 -- 35 (W--) ------------------------ log hav 9.48368 L.A.T.(t) 17d -- 19h -- 32m -- 02s log cos 9.87446 Lat. 41 deg. 30' N log cos 9.97473 Dec. 19 deg. 21' 25" N -------- log hav S 9.33287 N s .21521 L - D 22 deg. 08' 35" N D +- L .03687 -------- Calc. ZD 60 deg. 16' 30" N ZD .25208 -- 90 deg. 00 00 ------------- TZ found from table to be Cal. Alt. 29 deg. 43' 30" N 90 deg. E. -(-)- 29 deg. 50' 04" ------------- Alt. Diff 6' 34" Toward.
_ Course. Dist. Diff. Lat. Dep. Diff. Lo._ 90 deg. 6' 34" 0 6.5 8.6
D.R. Lat. 41 deg. 30' N D.R. Lo. 33 deg. 38' 45" W Diff. Lat. -- Diff. Lo. 8 36 E ---------- ------------- Most probable fix Lat. 41 deg. 30' N Lo. 33 deg. 30' 09" W
As azimuth is N 90 deg. E, Line of Position runs due N & S (360 deg.) through Lat. 41 deg. 30' N. Lo. 33 deg. 30' 09" W.
Assign for work in class and for Night Work examples such as the following:
1. July 11th, 1919. (_) 45 deg. 35' 30", Lat. by D. R. 50 deg. 00' N, Lo. 40 deg. 04' W. HE 15 ft. IE--4'. CT (corrected) 5h. 38m 00s P.M. Required Line of Position by Marc St. Hilaire Method and most probable fix of ship.
2. May 16th, 1919, A.M. (_) 64 deg. 01' 15", D. R. Lat. 39 deg. 45' N, Lo. 60 deg. 29' W. HE 36 ft. IE + 2' 30". CT 2h 44m 19s. Required Line of Position by Marc St. Hilaire Method and most probable fix of ship.
Etc.
SATURDAY LECTURE
EXAMPLES ON MARC ST. HILAIRE METHOD BY A SUN SIGHT
1. Nov. 1st, 1919. A.M. at ship. WT 9h 40m 15s. C--W 4h 54m 00s. D. R. Lat. 40 deg. 50' N, Lo. 73 deg. 50' W. (_) 27 deg. 59'. HE 14 ft. Required Line of Position by Marc St. Hilaire Method and most probable position of ship.
2. May 30th, 1919. P.M. at ship. D. R. Lat. 38ยบ 14' 33" N, Lo. 15 deg. 38' 49' W. The mean of a series of observations of (_) was 39 deg. 05' 40 deg.. IE--01' 00". HE 27 ft. WT 3h 4m 49s. C--W 1h 39m 55s. C.C. fast, 01m 52s. Required Line of Position by Marc St. Hilaire Method, and most probable position of ship.
3. Oct. 21st, 1919, A.M. D. R. Lat. 40 deg. 12' 38" N, Lo. 69 deg. 48' 54" W. The mean of a series of observations of (_) was 19 deg. 21' 20". IE + 02' 10". HE 26 ft. WT 7h 58m 49s. C--W 4h 51m 45s. C. slow, 03m 03s. Required Line of Position by Marc St. Hilaire Method and most probable position of ship.
4. June 1st, 1919, P.M. at ship. Lat. D. R. 35 deg. 26' 15" S, Lo. 10 deg. 19' 50" W. W.T. 3h 30m 00s. C--W 0h 20m 38s. CC 1m 16s slow. (_) 16 deg. 15' 40". IE + 2' 10". HE 26 ft. Required Line of Position and most probable fix of ship.
5. Jan. 5th, 1919. A.M. D. R. Lat. 36 deg. 29' 38" N, Lo. 51 deg. 07' 44" W. The mean of a series of observations of (_) was 23 deg. 17' 20". IE + 01' 50". HE 19 ft. WT 7h 11m 37s. C--W 5h 59m 49s. C. slow 58s. Required Line of Position and most probable fix of ship.
WEEK V--NAVIGATION
TUESDAY LECTURE
A SHORT TALK ON THE PLANETS AND STARS IDENTIFICATION OF STARS
_1. The Planets_
You should acquaint yourself with the names of the planets and their symbols. These can be found opposite Page 1 in the Nautical Almanac. All the planets differ greatly in size and in physical condition. Three of them--Mercury, Venus and Mars--are somewhat like the earth in size and in general characteristics. So far as we know, they are solid, cool bodies similar to the earth and like the earth, surrounded by atmospheres of cool vapors. The outer planets on the other hand, i.e., Jupiter, Saturn, Uranus, and Neptune, are tremendously large--many times the size of the earth, and resemble the sun more than the earth in their physical appearance and condition. They are globes of gases and vapors so hot as to be practically self luminous. They probably contain a small solid nucleus, but the greater part of them is nothing but an immense gaseous atmosphere filled with minute liquid particles and heated to an almost unbelievably high temperature.
Of the actual surface conditions on Venus and Mercury, little is definitely known. Mercury is a very difficult object to observe on account of its proximity to the sun. It is never visible at night; it must be examined in the twilight just before sunrise or just after sunset, or in the full daylight. In either case the glare of the sun renders the planet indistinct, and the heat of the sun disturbs our atmosphere so as to make accurate visibility almost impossible. The surface of Mercury is probably rough and irregular and much like the moon. Like the moon, too, it has practically no atmosphere. Mercury rotates on its axis once in 88 days. Its day and year are of the same length. Thus the planet always presents the same face toward the sun and on that side there is perpetual day while on the other side is night--unbroken and cold beyond all imagination.
Venus resembles the earth more nearly than any other heavenly body. Its diameter is within 120 miles of the earth's diameter. The exasperating fact about Venus, however, is that it is shrouded in deep banks of clouds and vapors which make it impossible for us to secure any definite facts about it. The atmosphere about Venus is so dense that sunlight is reflected from the upper surface of the clouds around the planet and so reaches our telescopes without having penetrated to the surface at all. From time to time markings have been discovered that at first seemed real but whether they are just clouds or tops of mountains has never really been established.
Of all the planets, we know more about Mars than any other. And yet practically nothing is actually known in regard to conditions on the surface of this planet. We do know, however, that Mars more nearly resembles a miniature of our earth than any other celestial body. The diameter of Mars is 4,210 miles--almost exactly half the earth's diameter. The surface area of Mars is just about equal to the total area of dry land on the earth. Like the earth, Mars rotates about an axis inclined to the plane of its orbit, and the length of a Martian day is very nearly equal to our own. The latest determinations give the length of a Martian solar day as 24h 39m 35s. Fortunately for us, Mars is surrounded by a very light and transparent atmosphere through which we are able to discover with our telescopes, many permanent facts.
The most noticeable of these are the dazzling white "polar caps" first identified by Sir William Herschel in 1784. During the long winter in the northern hemisphere, the cap at the North pole steadily increases in size, only to diminish during the next summer under the hot rays of the sun. These discoveries establish without doubt the presence of vapors in the Martian atmosphere which precipitate with cold and evaporate with heat. The polar caps, then, are some form of snow and ice or possible hoar frost. Outside the polar caps the surface of Mars is rough, uneven and of different colors. Some of the darker markings appear to be long, straight hollows. They are the so-called "canals" discovered by Schiaparelli in 1877. The term "canal" is an unfortunate one. The word implies the existence of water and the presence of beings of sufficient intelligence and mechanical ability to construct elaborate works. Flammarion in France and Lowell in the United States claim the word is correctly used, i.e., that these markings are really canals and that Mars is actually inhabited. The consensus of opinion among the most celebrated astronomers is contrary to this view. Most astronomers agree that these canals may not exist as drawn--that they are to great extent due to defective vision. There is no conclusive proof of man-made work on Mars, nor of the existence of conscious life of any kind. It may be there but conclusive proof of it is still lacking.
_2. The Stars_
The planets are often called wanderers in the sky because of their ever changing position. Sharply distinguished from them, therefore, are the "fixed" stars. These appear as mere points of light and always maintain the same relative positions in the heavens. Thousands of years ago the "Great Dipper" hung in the northern sky just as it will hang tonight and as it will hang for thousands of years to come. Yet these bodies are not actually fixed in space. In reality they are all in rapid motion, some moving one way and some another. It is their tremendous distance from us that makes this motion inappreciable. The sun seems far away from us, but the nearest star is 200,000 times as far away from us as is the sun. Expressed in miles, the figure is so huge as to be incomprehensible. A special unit has, therefore, been invented--a unit represented by the distance traversed by light in one year. In one second, light travels over 186,000 miles. In 8-1/3 minutes, light reaches us from the sun and, in doing so, covers the distance that would take the Vaterland over four centuries to travel. Yet the nearest star is over four "light years" distant--it is so far away that it requires over four years for its light to reach us. When you look at the stars tonight you see them, not as they are, but as they were, even centuries ago. Polaris, for instance, is distant some sixty "light years." Had it disappeared from the heavens at the time Lee surrendered to Grant, we should still be seeing it and entirely unaware of its disappearance.
Now each star in the heavens is in reality a sun, i.e., a vast globe of gas and vapor, intensely hot and in a continuous state of violent agitation, radiating forth heat and light, every pulsation of which is felt throughout the universe. So closely indeed do many of the stars resemble the sun, that the light which they emit cannot be distinguished from sunlight. Some of them are larger and hotter than the sun--some smaller and cooler. Yet the sun we see can be regarded as a typical star and from our knowledge of it we can form a fairly correct idea of the nature and characteristics of these other stars.
Anyone knows that the stars vary in brightness. Some of this variation is due partly to actual differences among the stars themselves and partly to varying distances. If all the stars were alike, then those which were farthest away would be faintest and we could judge a star's distance by its brilliancy. This is not the case, however. Some of the more brilliant stars are far more distant than some of the fainter ones. There are stars near and remote and an apparently faint star may in reality be larger and more brilliant than a star of the first magnitude. Vega, for instance, is infinitely farther away from us than the sun, yet its brightness is more than 50 times that of the sun. Polaris, still farther away, has 100 times the light and heat of the sun. In fact the sun, considered as a star, is relatively small and feeble.
_3. Identification of Stars_
Only the brighter stars can be used in navigation. So much light is lost in the double reflection in the mirrors of the sextant, that stars fainter than the third magnitude can seldom be observed. This reduces the number of stars available for navigation to within very narrow limits, for there are only 142 stars all told which are of the third magnitude or brighter. The Nautical Almanac gives a list of some 150 stars which may be used, but as a matter of fact, the list might be reduced to some 50 or 60 without serious detriment to the practical navigator. About 30 of these are of the second magnitude or greater and hence easily found. It is not difficult to learn to know 30 or 40 of the brighter stars, so that they can be recognized at any time. To aid in locating the stars, many different star charts and atlases have been published, but most of them are so elaborate that they confuse as much as they help. The simpler the chart, the fewer stars it pretends to locate, the better for practical purposes. Also, all charts are of necessity printed on a flat surface and such a surface can never represent in their true values, all parts of a sphere. A chart, therefore, which covers a large part of the heavens, is bound to give a distorted idea of distances or directions in some part of the sky and must be used with caution.
There are a few stars which form striking figures of one kind or another. These can always be easily located and form a starting point, so to speak, from which to begin a search for other stars. Of these groups the Great Dipper is the most prominent in the northern sky and beginning with this the other constellations can be located one by one.
When the groups or constellations are not known, then any individual star can be readily found by means of its Right Ascension, and Declination. As you have already learned, Declination is equivalent to latitude on the earth and Right Ascension practically equivalent to longitude on the earth, except that whereas longitude on the earth is measured E. and W. from Greenwich, Right Ascension is measured to the east all the way around the sky, from the First Point of Aries. With this in mind, you can easily see that if a star's R.A. is less than yours, i.e., less than L.S.T. or the R.A. of your Meridian, the star is not as far eastward in the heavens, as is your zenith. In other words it is to the west of you. And vice versa, if the Star's R.A. is greater than yours, the Star is more to the eastward than you and hence to the east of you. Moreover, as R.A. is reckoned all around a circle and in hours, each hour's difference between the Star's R.A. and yours is 1/24 of 360 deg. or 15 deg.. Hence if a star's R.A. is, for instance, 2 hours greater than yours, the star will be found to the east of your meridian and approximately 30 deg. from your meridian, providing the star is in approximately the same vertical east and west plane as is your zenith.
When the general east or west direction of any star has been determined, its north or south position can at once be found from its declination. If you are in Latitude 40 deg. N. your celestial horizon to the South will be 90 deg. from 40 deg. N. or 50 deg. S. and to the North it will be 90 deg. + 40 deg. N. = 130 deg. or 40 deg. N. (below the N. pole). The general position of the equator in the sky is always readily found according to the latitude you are in. If you are in 40 deg. N. latitude, the celestial equator would intersect the celestial sphere at a point 40 deg. South of you. Knowing this, the angular distance of a star North or South of the equator (which is its declination) should be easily found. Remember, however, that the equator in the sky is a curved line and hence a star in the East or West which looks to be slightly North of you may actually be South of you.
Put in your Note-Book:
If the star is west of you its R.A. is less than yours. If east of you, its R.A. is greater than yours. Star will be found approximately 15 deg. to east or west of you for each hourly difference between the star's R.A. and your R.A. (L.S.T.).
Having established the star's general east and west direction, its north and south position can be found from its declination.
_4. Time of Meridian Passage of a Star_
It is often invaluable to know first, when a certain star will be on your meridian or second, what star will be on your meridian at a certain specified time. Here is the formula for each case, which put in your Note Book:
1. To find when a certain star will cross your meridian, take from the Nautical Almanac, the R.A. of the Mean Sun for Greenwich Mean Noon of the proper astronomical day. Apply to it the correction for longitude in time (West +, East -) as per Table at bottom of page 2, Nautical Almanac, and the result will be the R.A. of the Mean Sun at local mean noon, i.e., the distance in sidereal time the mean sun is from the First Point of Aries when it is on your meridian. Subtract this from the star's R.A., i.e., the distance in sidereal time the star is from the First Point of Aries (adding 24 hours to the star's R.A., if necessary to make the subtraction possible). The result will be the distance in sidereal time the star is from your meridian i.e., the time interval from local mean noon expressed in units of sidereal time. Convert this sidereal time interval into a mean time interval by always subtracting the reduction for the proper number of hours, minutes and seconds as given in Table 8, Bowditch. The result will be the local mean time of the star's meridian passage.
Example:
April 22nd, 1919, A.M. at ship. In Lo. 75 deg. E. What is the local mean time of the Star Etamin's meridian passage?
R.A.M.S. Gr. 21d--0h 1h--54m--02s Red. for 75 deg. E (--5h) --49.3 ________________
R.A.M.S. local mean noon 1h--53m--12.7s
Star's R.A. 17h--54m--44s -- 1 --53 --12.7 ___________________
Sidereal interval from L.M. Noon 16h--01m--31.3s Red. for Sid. Int. (Table 8) -- 2 --37.3 ___________________ L.M.T. 21 d 15h--58m--54s
Hence, star will cross meridian at 3h--58m--54s A.M. April 22nd.
2. To find at any hour desired what star will cross your meridian, take the R.A. of the Mean Sun for Greenwich Mean Noon of the proper astronomical day. Apply to it the correction for longitude in time (West +, East -) as per table at bottom of page 2, Nautical Almanac, and the result will be the R.A. of the Mean Sun at local mean noon; i.e., the distance in sidereal time the mean sun is from the First Point of Aries when it is on your meridian. Suppose you wish to find the star at 10 P.M. Add 10 sidereal hours to the sun's R.A. just found. The result will be the R.A. of your meridian at approximately 10 P.M.