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EXAMPLE NUMBER II

Find the course and distance from Cape Horn in latitude 55° 58'41" S. and longitude 67° 16' 15" W. to Sydney, Australia, in latitude 33° 51' 41" S. and longitude 151° 12' 23" E.

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sec.

Co. N. 77° 22' W.
Prop. dif. lat.
Dist.

.66013 1327'.0 + 3.12287 6067.4 = 3.78300 EXPLANATION

Find the difference of latitude by subtracting the latitude of Sydney from that of Cape Horn, convert it into miles and name it north because Sydney is north of Cape Horn.

From Table 3 take the meridional parts for the latitudes to the nearest mile and find their difference, which is the meridional difference of latitude and takes the same name as the proper difference of latitude.

To the longitude of Cape Horn add the longitude of Sydney because they are of different name and the result will be the difference of longitude east, and as it is greater than 180°, it is subtracted from 360° and gives the difference of longitude 8491'.4 W.

The middle latitude should not be found in the usual manner, if an accurate result is required.

From the logarithm of the proper difference of latitude 1327'. subtract the logarithm of the meridional difference of latitude 1903.9, which gives the logarithm cosine of the middle latitude 45° 49'.

To the logarithm of the difference of longitude 8491'.4 add the logarithm cosine of the middle latitude 45° 40' and from the resulting logarithm subtract the logarithm of the proper difference of latitude 1327'.0, which gives the logarithm tangent of the course N. 77° 22' W.

To the logarithm secant of the course N. 77° 22' W. add the logarithm of the proper difference of latitude 1327'.0, which gives the logarithm of the distance 6067.4.

MERCATOR SAILING BY INSPECTION

Having the latitudes and longitudes of the two points between which the course and distance are wanted, find their differences and name the difference of latitude north or south and the difference of longitude east or west, according to the direction of the point to which the course and distance is to be found.

From Table 3 take the meridional parts for each latitude to the nearest mile and find their difference, which takes the same name given the proper difference of latitude.

Enter Table 2 with the meridional difference of latitude and difference of longitude and the course will be found where they agree nearest, the meridional difference of latitude in the latitude column and the difference of longitude in the departure column. If the meridional difference is the greater, the course will be at the top of the page, and if the difference of longitude is the greater, the course will be found at the bottom of the page; but in any case they do not give the distance.

The distance will be found in the distance column opposite the proper difference of latitude in the latitude column under the same degree where the course is found, taking care to read from the same end of the page, top or bottom, from which the course was taken.

EXAMPLE NUMBER I

Both latitudes and longitudes to find the course and distance: A ship is in latitude 36° 51'00" N. and longitude 70° 55' 45" W. Find the course and distance to Barnegat light in latitude 39° 45' 52" N. and longitude 74° 06' 24" W.

Lat. ship

- 36° 51'00" N. Lat. Barnegat

39 45 52 N. Dif. 174.9 =

2 54 52 N.

Mer. parts
Mer. parts
Dif.

- 2367'.:3 2589.5 222 .2 N.

Long. ship

- 70° 55' 45" W. Long. Barnegat 74 06 24 W Dif.

1909.65 = 3 10 39 W.

Mer. dif. 222'.2 N.

Dif. long: 190.6 W; } =Co. N. 41° W.

} = Distance 232.0.

Co. N. 41° W.
Prop. dif. lat. 174.9

EXPLANATION

Find the difference of latitude by subtracting the latitude of the ship from that of Barnegat light, convert it into miles and name it north because Barnegat light is north of the latitude of the ship.

Find the difference of longitude by subtracting the longitude of the ship from that of Barnegat light, convert it into miles and name it west because Barnegat light is west of the longitude of the ship.

From Table 3 take the meridional parts for the latitudes to the nearest mile and find their difference, which is the meridional difference of latitude and takes the same name as the proper difference of latitude.

Enter Table 2 with the meridional difference of latitude 222'.2 N. and the difference of longitude 190°.6 W. and where they are found to agree nearly, the meridional difference in the latitude column and the difference of longitude in the departure column will give the course N. 41° W.

The course N. 41° W. and the proper difference of latitude 174.9 in the latitude column will give the distance 232'.O.

EXAMPLE NUMBER 2

Both latitudes, one longitude and departure to find the course and distance, and longitude in: A ship left a point in latitude 37° 55' 25" N. and longitude 74° 56' 22" W. and arrived in latitude 35° 57' 25" N., the departure being 216':5 E. Find the course and distance and longitude of the ship.

Lat. point

37° 55' 25" N. Lat. ship.

- 35 57 25 N. Dif. 118.0= 1 58 00 S.

Mer. parts
Mer. parts
Dif.

2447'.5 2300.5

147.0 S.

Proper. dif. lat. 118.0 :} = Co. S. 61° 30' E.

}

Co. S. 61° 30' E.
Mer. dif. lat. 147'.

= dif. long. 270'.6 E.

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Find the difference of latitude by subtracting the latitude of the ship from that of the point left, convert it into miles and name it south because it is south of the point sailed from.

From Table 3 take the meridional parts to the nearest mile of latitude and take their difference, which takes the same name as the proper difference of latitude.

Enter Table 2 wi the proper difference of latitude 118.0 S. and departure 216.5 E. and where they agree nearly, the course

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