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 Latitude. Find the algebraic difference between Longitude in and Longitude sought and call this difference of Longitude. With the Meridional difference of Latitude and the difference of Longitude, find the course by searching in Table 2 for the page where they stand opposite each other in the latitude and departure columns. Now find the real difference of latitude. Under the course just found and opposite the real difference of Latitude, 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 Latitude 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 latitude, meridional difference of latitude and the difference of longitude. Reduce real difference of latitude 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 latitude, 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.
Assign for Night Reading Arts, in Bowditch: 183-184-185-186-187-188-189-194-259-260-261-262-263-264-265-266-267-268.
Also, one of the examples of Mercator sailing to be done by both the Inspection and Logarithmic method.