Or the length can be found by multiplying the number of inches representing 40' of longitude by the secant of the middle latitude. To find the number of inches for 40' of Long. 60': 6" :: 40' : x To find the number of inches between 50° N. and 50° 40' N. 4 in. log. 0:602060 Middle lat. 50° 20' sec. 10:194961 Length between 50°N. and 50° 40' N. is 6.27 inches. 6-27 log. 0-797021 METHOD OF CONSTRUCTING A MERCATOR'S CHART For the sake of the younger students it may be advisable to notice the following points. On the sphere the distance between the meridians decreases from the equator towards the pole, where they all meet, whilst the parallels of latitude are everywhere practically the same distance apart. Now on a Mercator's Chart the meridians are the same distance apart in all latitudes, but the distance between the parallels increases from the equator towards the pole in the same ratio as the distance between the meridians has been increased ; that is, as the secant of the latitude. The meridional parts between any two parallels are found by multiplying a degree of longitude at the equator by the secant of the middle latitude. For example : find the meridional parts between 47° N. and 48° N. The middle latitude is 47to, and 60' x sec: 471° = 88.82 minutes of longitude. It would serve no useful purpose to multiply i minute of longitude by 47° 1', 47° 2', etc., up to 48°, and taking the sum of all the products, because by using the secant of the middle latitude the result is, for all practical purposes, the same. It is obvious from what has been said that all distances measured on a chart on Mercator's Projection must be measured on the graduated meridian in the latitude in which the ship is. On a Mercator's Chart the mile of latitude the minute of long. X sec. lat. ::. minute of long mile of lat. X cos. lat. One minute of longitude at the equator is called a geographical mile and contains 6,086 feet. It is very nearly equal to the average length of a minute of latitude. The length of a minute of latitude at the equator is 6,043:4 feet and at the poles 6,128-6 feet, and the mean length 6,080 feet. Construct a Mercator's Chart on a scale of 6 inches to a degree of longitude extending from lat. 47° N. to lat. 50° N. and from long. 20° W. to long. 25° W. Method I, using Meridional Parts Lat. 48° mer. pts. 3291:53 Lat. 49o mer. pts. 3382.08 47° 3202.71 3291.53 Mer. pts. between Mer. pts. between · 47o and 480 88.82 48° and 49° 90.55 48° . Lat. 50° mer. pts. 3474:47 49° 3382.09 Mer. pts. between 49° and 50o = 92.38 Meridional parts are minutes of longitude at the equator. 90':55 48° 49° 49° 50° Or the length between the parallels can be found by multiplying the longitude scale by the secant of the middle latitude. FormulaLat. scale long. scale X sec. middle lat. Long. scale 6" log. 0:778151 8.881 ins. log. 8468 6" log. 0-778151 481° sec. 10.178735 9.055 ins. log. 0.956886 6" log. 0.778151 491° sec. 10.187456 9.238 ins. log. O•$65607 The length of the chart equals 8.881 ins. + 9.055 ins. + 9.238 ins, = 27.174 inches, and the breadth equals 30 inches, and would be shown thus : 27.174 X 30. The natural scale is found as follows The latitude scale is 9.055 inches to a degree of middle latitude, and using the mean length of a minute of latitude the natural scale would equal the number of inches in one degree divided by the number of inches in the scale degree of middle latitude. I 4377600 inches = 9:055 = 483444, therefore the natural scale is 483444 Test the accuracy of the calculations for the meridional length of the chart by finding the meridional difference between the two extreme latitudes and multiplying it by the longitude scale and dividing by 60; the result should be equal to the sum of the separate calculations Lat. 47° mer. pts. 3202-71 3474:47 50° 271.76 x 6 = 27.176 271076 The meridional length is 27.176 inches, practically the same as above. To draw the Chart. Draw a horizontal line near the lower edge of the paper to represent the parallel of 47° N.; divide this parallel into five equal parts of six inches each to represent the degrees of longitude, and number them 20°, 21°, 22°, 23°, 24°. and 25° Commencing on the right, at 20° and 25° erect, very carefully, perpendiculars 27.176 inches long and draw through the two points reached a line parallel to the parallel of 47° N., and it will be the parallel of 30° S. To put in the parallel of 48° take 8.88 inches or 88.8 minutes of longitude from the graduated parallel, and with one leg on the parallel of 47° N. and the meridian of 20° W., the other leg will find the position of the parallel of.:8°N, This distance can be laid off on each meridian and the parallel drawn with the parallel rulers. The position of the parallel of 49° N. is found in a similar manner. Draw the meridians of 22°, 23°, and 24° W. and graduate the meridian for latitude and distance and the parallels at the top and bottom for longitude and meridional parts. For the purpose of graduating the latitude and longitude scales the proportional compasses are most useful. The inner, margin of the chart is called the frame. At a distance of about 1 of an inch from the frame, and outside of it, draw another line parallel to the frame; the graduations come between this outer line and the frame. Draw a compass on the magnetic or true meridian, subdividing it to degrees or points as required, and finish according to individual taste. Tire framework of the chart can be tested as follows: Measure the diagonals and if they are equal the framework is correct, as a rectangular, parallelogram alone has its two diagonals equal in length, and a Mercator's Chart is a rectangular parallelogram. DESCRIPTION AND USE OF CHARTS Charts are marine maps, representing the whole or part of the surface of the water and adjoining coasts ; exhibiting islands, rocks, shoals, banks, depths of water, the variation of the compass, and whatever other particulars may serve to direct the mariner on his voyage, or point out the dangers to be avoided. If you take a globe and try to find the course and distance between any two places, you will experience considerable difficulty in ascertaining. what you require, and you would find it impossible to do so on a map constructed on the globular projection. The early navigators had to contend with this difficulty, and projected what they called the plane chart, on which the parallels and meridians were equidistant straight lines. Gerard Kauffman (better known as Mercator) devised the method to which his name has been given. The system was brought to perfection by Edward Wright of Garveston, Norfolk, in 1594. The Mercator Chart is now universally used for general navigation; the parallels and meridians are straight lines; the meridians are equidistant, but the parallels are graduated. The construction is such that rhumbs are also represented by straight lines. The parallels of latitude on the surface of a globe are everywhere equidistant, but the distance between the meridians lessens towards the poles. It may be seen that if on a plane surface the parallels are retained equidistant while the meridians are spread at the poles to the distance they have at the equator, there must be considerable distortion. But the difficulty is got over, and the relation between the different parts preserved by widening the distance between the parallels of latitude to the same proportionate extent that the meridians have been widened. It matters not that the extent of land and water in the higher latitudes is out of proportion with the equatorial regions; the shape is still approximately preserved, and—what is of most importance in navigationthe relative direction from one part to another, and hence the track of a ship steering the same course can be drawn as a straight line. Charts are drawn on a large or small scale. It will be a large scale if a small part of the coast is delineated or on a small scale if a large part of the coast is delineated. A Plan is a chart that comprises a detached portion of a general chart on a large scale, as a harbour, roadstead, small bay, the entrance to a river, channels leading to a port, a small part of a sea where the navigation is intricate. Such a chart only occasionally shows parallels and meridians; when these are absent, a scale of miles and longitude is given. USE OF MERCATOR'S CHART When a chart is properly spread out before you, so that you can read it like the page of a book, the top is the north, the bottom is the south, the side to the right is the east, and the side to the left is the west. The |