# Mercator sailings

##### Scale of a Mercator chart.

Because the equator is shown on a Mercator chart as a straight line of definite length and the meridians appear as straight lines perpendicular to it, the longitude scale is fixed by that length and is constant in all latitudes. The latitude scale, on the other hand, is not constant. Since the meridians appear on a Mercator chart as parallel straight lines instead of the converging lines they are in reality, the chart is increasingly distorted the further one moves from the equator. To cater for this distortion, the scale of the latitude has to be increasingly enlarged the further north or south one goes. Mathematically, it has been established that this distortion in any latitude is governed by the secant of the latitude.

Mercator charts are graduated along the left- and right- hand edges for latitude and distance and along the top and bottom edges for longitude. It is important to note that the longitude scale is only used for laying down or taking off the longitude of a place, never for measuring distance.

##### Measurement of distance on a chart.

Because the latitude scale is not constant, care must be taken when measuring distance from the left- and right-hand edges of the chart. The distance must be measured around the middle latitude between the two points.

##### Meridional parts.

Since the latitude and distance scale at any point on a Mercator charts is proportional to the secant of the latitude of that part, the scale continually increases as it recedes from the equator, until at the poles it becomes infinite. The latitude scale therefore, affords no ready means of comparison with the fixed longitude scale. In order to use the units measured on the latitude and longitude scale in relation to one another, ie as entities in a mathematical formula, they need to be measured in the same fixed units. The fixed longitude scale provides this unit, which is the length of 1’ of arc on that scale. The length is the meridional part, which is defined as follows:
The meridional parts of any latitude are the number of longitude units in the length of a meridian between the parallel of that latitude and the equator.

##### Meridional part tables.

Meridional parts are involved with chart lengths and not in any way connected with distance on the earth’s surface, which is measured in nautical miles. Where does one find the meridional parts of any latitude? In Nories tables, where they are given with allowance for the spheroid shape of the earth.

##### Difference of meridional parts (DMP).

Where the start point of a voyage does not start on the equator, its latitude also has mer parts. The difference between the mer parts of the latitudes of the starting point and the destination, are called the difference of mer parts and written DMP. If both points lie on the same side of the equator, then their mer parts are subtracted from each other. If they lie on opposite sides of the equator, they are added to one another.

To find the course and distance by Mercator sailing. In determining the course and distance between positions using the Mercator sailing method, we make use of two formulae, namely:

The following triangles illustrate how these formulae were derived:

Angle DAC is the azimuth, side AE is the distance, side AB is the d’lat, side DC is the d’long and side AC is the difference of meridional parts.

With the Mercator sailing method, the course is determined first by the use of the first formula. The answer will be an azimuth and must be converted to a true course. See the instructions contained in the section on plane sailing. Once you have the course, it together with the d.lat is used in formula two to derive the distance to be covered. Remember when using the course in the second formula, it actually means the azimuth which you obtained via the first formula.
As a guide, a pro-forma of the method used is shown below as Appendix D, entitled “Mercator Sailing”.

Appendix D