CASE 2.

77. Given the MERIDIAN DISTANCE between two places in the same PARALLEL OF LATITUDE, to find the DIFFERENCE OF

LONGITUDE.

Rule. Set the index on the given parallel, and the meridian distance taken on the equator, will give the difference of longitude on the index.

Example. The meridian distance between two places in the parallel of 36 deg. of lat. is 110 milesrequired the difference of longitude.

Here the index set on 36 deg. of lat. 110 on the equator gives on the index 136 the difference of longitude. A ship in lat. 48 deg. sails west 150 miles, what is her difference of longitude? Ans. 224 miles.

A ship in lat. 32 deg. sails east 117 miles, what is her difference of longitude? A ship in lat. 10 deg. sails west 60 difference of longitude?

A ship on the equator sails east her difference of longitude?

CASE 3.

Ans. 138 miles.
miles, what is her
Ans. 61 miles.
60 miles, what is
Ans. 60 miles.

78. Given the DIFFERENCE of LONGITUDE and the MERIDLAN DISTANCE, to find the PARALLEL of LATITUDE.

Rule.-Set the index to meet the difference of longitude with the meridian distance, it will be on the parallel of latitude.

Example.-A ship sails east 105 miles, and her diff. of lon. is 120-required the latitude sailed in.

Here the diff. of lon. 120 with the meridian distance 105 give the latitude 29 deg.

A ship sails west 115 miles, and her diff. of lon. is 146, what is the latitude?

A ship sails east 125 miles, and her 203, what is the latitude?

Ans. 38 deg.. diff. of lon. is Ans. 52 deg.

MIDDLE LATITUDE SAILING.

79. In middle latitude sailing the earth is considered a globe, as in parallel sailing.

80. It is compounded of plane and of parallel sailing, the middle latitude being substituted as an artificial parallel, by which the departure, found by the rules in plane sailing, is reduced to longitude by the rules in parallel sailing.

81. The middle latitude is the half sum of the two latitudes, when they are both on the same side of the equator; but when the latitudes are on each side of the equator, it is half the difference of the two latitudes.

82. There are seven cases; and in which these six terms are used, viz: course, distance, difference ‘of latitude, departure, difference of longitude, and middle latitude..

CASE 1.

$3. Given—the LATITUDES and the LONGITUDES of two places to find the COURSE and DISTANCE.

Rule. Set the index on the middle latitude; and from the difference of longitude, taken on the index trace the nearest line to the equator for the departure ; then the difference of latitude, and the departure will give the course and distance, as in case 6, plane sailing.

Example. What is the course and distance from Cape Cod Light-house in lat. 42 deg. 05 N. lon. 70 d.. 04 W. and Mt. Desert Rock in lat. 43 deg. 52 N. and Hon.. 68 d. 09 W. ?

Here the index set on the middle lat. 42 deg. 58 (or 43 deg.) the diff. lon. 115 on the index gives the departure 84 on the equator; then the diff. lat. 107 and the departure 84, give the course 38

deg. or N. 38 deg. 12 m. E. and the distance 136 miles.

CASE 2.

84. Given both LATITUDES and the DEPARTURE, to find the COURSE, DISTANCE, and DIFFERENCE OF LONGITUDE. Rule.-Set the index to meet the difference of latitude with the departure, it will give the course and distance; then set the index on the middle latitude, and the departure on the equator will give the difference of longitude on the index.

Example.-A ship in lat. 42 deg. N. sails northeasterly till her diff. of lat. is 180 miles, and her departure 104; required the course, distance, and the difference of longitude.

Here the diff. lat. 180 and the dep. 104 give the course N. 30 deg. E. and the distance 208 miles; then the middle lat. 43 deg. 30 m. and the departure 104 give the diff. of lon. 143 miles.

CASE 3.

85. Given-one LATITUDE, the COURSE and the DISTANCE, to find the DIFF. OF LAT. the DEPARTURE, and the DIFF.

OF LONGITUDE.

Rule. The course and distance give the diff. of lat. and the dep. as by case 1 plane sailing; then the middle lat. and the dep. give the diff. of lon.

Example. A ship in lat. 34 deg. N. sails N. 3 points W. 193 miles; required the diff. of lat. the departure, and the diff. of lon.

Here the course 34 points and the distance 193 give the diff. lat. 155, and the departure 115; hence the lat. is in 36 deg. 35 m. N. and the mid. lat. is 35 deg. 18,

which with the departure 115 give the diff. of lon. 141.

miles.

CASE 4.

86. Given both LATITUDES and the COURSE, to find the DISTANCE, the DEPARTURE, and the DIFF. OF LON.

Rule. Set the index on the course, and the diff. lat. will give the distance and the departure; then set the index on the middle latitude, and the departure will give the diff. of lon.

Example.-A ship in lat. 44 deg. N. sails N. 5 points W. till she is in lat. 46 deg. N.; required the distance, the departure, and the diff. of lon.

Here the course 5 points and the diff. lat. 120 give the distance 216 miles, and the departure 1794; then the middle lat. 45 deg. and the dep. 179 give the difference of lon. 254 miles.

CASE 5.

87. Given both LATITUDES and the DISTANCE to find the COURSE, DEPARTURE, and DIFF. of Longitude.

Rule. Set the index to meet the diff. of lat. with the distance, it will give the course and departure ; and the middle latitude with the departure will give the difference of longitude.

Example.-A ship in lat. 28 deg. N. sails northeasterly 217 miles, and is in lat. 31 deg. 04 m. N. required the course, departure, and difference of longitude.

Here the distance 217 with the diff. lat. 184 give the course N. 32° E. and the departure 115; which with the middle lat. 29 deg. 32 m. give the diff. of longitude 132 miles.

CASE 6.

88. Given one LATITUDE the COURSE and DEPARTURE, to find the DISTANCE, DIFF. LAT. and DIFF. LON.

Rule.-Set the index on the course, and the departure will give the distance and diff. of lat.; then the departure and middle latitude will give the diff. of lon.

Example.-A ship in lat. 26 deg. N. sails N. 5 points W. till her departure is 172 miles; required the distance, the diff. of lat. and the diff. of lon.

Here the course 5 points and the departure 172 give the distance 207, and diff. of lat. 115; and the departure 172 with the middle lat. 26 deg. 58 m. (or 27 deg.) give the diff. of lon. 193.

CASE 7.

89. Given one LAT. DISTANCE and DEPARTURE, to find the COURSE, DIFF. Lat. and diff. of lon.

Rule. The distance and the departure will give the course, and diff. lat. ; and the departure and middle lat. will give the diff. lon.

Example.-A ship in lat. 42 deg. N. sails southeasterly 119 miles, and her departure is 54; required the course, diff. lat. and diff. lon.

Here the distance 119 with the departure 54 give the course S. 27 deg. E. and the diff. lat. 106; and the middle lat. 41 deg. 07 m. with the departure 54 give the diff. lon. 72 miles.

MERCATOR'S SAILING.

90. In Mercator's sailing the earth is considered as an extended plane, infinite in length, and in breadth equal to the earth's circumference at the equator.

91. This projection was invented in 1566 by Gerard Mercator; its object is to represent on a plane the

4