Lectures in Navigation Part 6

Lat. left 39-46'-00" N Mid. Lat. 39 Diff. Lat. 1 -04 -06 S Dep. 71.5 ---------- Lat. in. 38 -41 -54 N Table 2--Under 39 Dep. in 39 -46 -00 Diff. Lat. col. = 92' = 1 32' Diff. Lo.

---------- 2)78 -27 -54 ---------- Mid. Lat. 39 -13 -57

Lo. left 74-06'-00" W Diff. Lo. 1 -32 -00 E -------------- Lo. in. 72-34'-00" W

Table 2--Diff. Lat. 64.1, Dep. 71.5.

Course S 48 E--Distance 96 miles.

The rule covering all these operations is as follows:

1. Write out the various courses with their corrections for Leeway, Deviation, Variation and the distance run on each.

2. In four adjoining columns headed N, S, E, W respectively, put down the Difference of Lat.i.tude and Departure for each course.

3. Add together all the northings, all the southings, all the eastings and all the westings. Subtract to find the difference between northings and southings and you will get the whole difference of Lat.i.tude. The difference between the eastings and westings will be the whole departure.

4. Find the lat.i.tude in, as already explained.

5. Find the Lo. in, as already explained.

6. With the whole difference of Lat.i.tude and whole Departure, seek in Table 2 for the page where the nearest agreement of Difference of Lat.i.tude and Departure can be found. The number of degrees at the top or bottom of the page (according as to whether the Diff. of Lat. or Dep. is greater) will give you the true course made good, and the number in the distance column opposite the proper Difference of Lat.i.tude and Departure will give you the distance made.

It is often convenient to use the reverse of the above method, i.e., being given the lat.i.tude and longitude of the position left and the lat.i.tude and longitude of the position arrived in, to find the course and distance between them by Middle Lat.i.tude Sailing. The full rule is as follows:

1. Find the algebraic difference between the lat.i.tudes and longitudes respectively.

2. Using the middle (or average) lat.i.tude as a course, find in Table 2 of Bowditch the Diff. of Lo. in the distance column. Opposite, in the Diff. of Lat. column, will be the correct Departure.

3. With the Diff. of Lat. between the position left and the position arrived in, and the Departure, just secured, seek in Table 2 for the page where the nearest agreement to these values can be found. On this page will be secured the true course and distance made, as explained in the preceding method.

4. Use this method only when steaming approximately an East and West course.

For an example of this method, see Bowditch, p. 77, example 3.

THURSDAY LECTURE

EXAMPLES ON PLANE AND TRAVERSE SAILING (_Continued_)

1. Departure taken from Cape Horn. Lat. 55 58' 41" S, Lo. 67 16' 15"

W, bearing by compa.s.s SSW 20 knots. s.h.i.+p heading SW x S, Deviation 4 E, steamed the following courses:

---------+----------+------------+-----------+---------- C. Cos. | Wind | Leeway | Deviation | Distance ---------+----------+------------+-----------+---------- SW x S | SE | 1 pt. | 4 E | 40 WNW | N | 2 pts. | 5 E | 25 S 40 E | NE | 2 pts. | 4 W | 20 ---------+----------+------------+-----------+----------

_Remarks_

Variation 18 E throughout. Current set NW magnetic 30 mi. for the day.

Required Lat.i.tude and Longitude in and course and distance made good.

2. Departure taken from St. Agnes Lighthouse, Scilly Islands, Lat. 49 53' S, Lo. 6 20' W, bearing by compa.s.s E x S, distance 18 knots, Deviation 10 W, Variation 23 W. s.h.i.+p headed N steamed on the following courses:

-------+------+-------+-------+------+------------------------------ C. Cos.| Wind |Leeway |Devia- |Dis- | Remarks | | |tion |tance | -------+------+-------+-------+------+------------------------------ N | | .. | 10 W | 60 |Variation 23 W. Current set S 1/2 E| W | 3 pts.| 10 E | 40 |SE mg 1-1/2 miles for 24 hrs.

NNE | NNW | 2 pts.| 8 W | 45 |Req. Lat. and Lo. in and | | | | |course and distance made | | | | |good, -------+------+-------+-------+------+------------------------------

a.s.sign for Night Work the following articles in Bowditch: 179-180-181-182. Also additional problems in Dead Reckoning.

FRIDAY LECTURE

MERCATOR SAILING

This is a method to find the true course and distance between two points. The method can be used in two ways, i.e., by the use of Tables 2 and 3 (called the inspection method) and by the use of logarithms. The first method is the quicker and will do for short distances. The second method, however, is more accurate in all cases, and particularly where the distances are great. The inspection method is as follows (Put in your Note-Book):

Find the algebraic difference between the meridional parts corresponding to the Lat. in and Lat. sought by Table 3. Call this Meridional difference of Lat.i.tude. Find the algebraic difference between Longitude in and Longitude sought and call this difference of Longitude. With the Meridional difference of Lat.i.tude and the difference of Longitude, find the course by searching in Table 2 for the page where they stand opposite each other in the lat.i.tude and departure columns. Now find the real difference of lat.i.tude. Under the course just found and opposite the _real_ difference of Lat.i.tude, will be found the distance sailed in the distance column. Example:

What is the course and distance from Lat. 40 28' N, Lo. 73 50' W, to Lat. 39 51' N, Lo. 72 45' W?

Lat. in 40 28' N Meridional pts. 2644.2 Lat. sought 39 51 N Meridional pts. 2596.0 --------- ------ 0 37' Mer. diff. Lat. 48.2

Lo. in 73 50' W Lo. sought 72 45 W --------- 1 05' = 65'

On page 604 Bowditch you will find 48.7 and 64.7 opposite each other, and as 48.7 is in the Lat. column only when you read from the bottom, the course is S 53 E. The real difference of Lat. under this course is opposite 62 in the distance column. Hence the distance to be sailed is 62 miles.

If distances are too great, divide meridional difference of Lat., real difference of Lat.i.tude and difference of Longitude by 10 or any other number to bring them within the scope of the distances in Table 2. When distance to be sailed is found, it must be multiplied by the same number. For instance, if the difference of Lat., difference of Lo., etc., are divided by 10 to bring them in the scope of Table 2, and with these figures 219 is the distance found, the real distance would be 10 times 219 or 2190.

Now let us work out the same problem by logarithms. This will acquaint us with two new Tables, i.e., Tables 42 and 44. Put this in your Note-Book:

Lat. in 40 28' N Mer. pts. 2644.2 Lo. in 73 50'

Lat. sought 39 51 Mer. pts. 2596.0 Lo. sought 72 45 --------- ------ ------- Real diff. 0 37' 48.2 1 05'

60 -- 60 5 -- (Table 42) log (+ 10) 65 = 11.81291 Log 48.2 = 1.68305 -------- Log tan TC (Table 44) 10.12986 TC = S 53 26' E

Log sec TC (53 26') = 10.22493 Log real diff. Lat. = 1.56820 + -------- 11.79313 - 10.

-------- 1.79313

Distance (Table 42) = 62.11 miles

Find algebraically the real difference of lat.i.tude, meridional difference of lat.i.tude and the difference of longitude. Reduce real difference of lat.i.tude and difference of longitude to minutes. Take log of the difference of longitude (Table 42) and add 10. From this log subtract the log of difference of meridional parts. The result will be the log tan of the True Course, which find in Table 44. On the same page find the log sec of true course. Add to this the log of the real difference of lat.i.tude, and if the result is more than 10, subtract 10.

This result will be the log of the distance sailed. This method should be used only when steaming approximately a North and South course.

Note.--For detailed explanation of Tables 42 and 44 see Bowditch, pp.

271-276.

a.s.sign for Night Reading Arts, in Bowditch: 183-184-185-186-187-188-189-194-259-260-261-262-263-264-265-266-267-268.