1863

19

20%:

10°

Sept

12

31

32°S.

difference of longitude=

By the middle latitude method, the formulæ are:

difference of departure × radius cosin mid-latitude

If the Mercatorial method be adopted, a table of Mercatorial or meridional differences of latitude must

be used, and the formulæ are:

difference of longitude-mer. diff. lat x diff. of departure.

difference of latitude

diff. of longitude x radius

;

tangent course=

mer. diff. latitude

Another mode is to obtain the course first, thus:

tangent course=

diff. of departure × radius

and afterwards obtain

difference of longitude:

=

diff. of latitude

mer. diff. lat. x tang. course radius

the distance being obtained as in the former case.

The Mercatorial method is well suited to the long distances performed at sea in 24 hours by steamers, and ships under favorable circumstances; but for the shorter distances travelled by land in journeys of eight or ten hours, the middle latitude method is sufficiently exact.

The resulting differences of latitude and longitude are checked by the results of astronomical observation, and by chronometers keeping Greenwich time; and thus

the error in position can be known within certain limits, even if the position itself is not fixed with sufficient certainty by these two modes of determination.

The method of reducing and calculating the daily courses of a vessel is illustrated by the examples actually worked out on the voyage which are given in Record No. V. at the end of the book.

Plotting the Route.

The plotting of a series of days' journeys may be made for nautical purposes on charts or chart-paper, having latitudes and longitudes drawn on the Mercatorial principle. These however possess, what is in the eyes of the landsman the defect, of not being scaleable anywhere with any scale of equal parts: hence for the traveller's purpose it is generally better to plot routes on maps or plans with the latitudes and longitudes laid down on the more simple principle shown in the attached sketch.

In this the lines of latitude are all equidistant parallel straight lines, while the lines of longitude are converging straight lines, the middle meridian alone being at right angles to the lines of latitude; the convergence is laid down thus. The value of a degree of longitude in miles at the upper latitude L is calculated=60 cos L, and these degrees are laid down to scale on the upper edge of the map; the value of a degree of longitude in miles. at the lower latitude L' is calculated 60 cosin L', and these degrees are laid down in the same way at the lower edge of the map. The corresponding degrees of longitude above and below are then joined by converging straight lines. Further exactitude may be obtained by

=