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Is to the Diff. of Lat. 777 , 2,89042 by Mid. Lat. Sailing without the

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1st, ‘Extend from Radius or 90°, to 46° 32' the Comp. Mid. Lat. on the Line of Sines, that Extent will reach from the Diff. of Long1192, to the Dep. 865, on the Line of Numbers.' .

2dly. ‘Extend from the Dep. 865, to the Diff. of Lat. 777 on the Line of Numbers, that Extent will reach from Radius or 45°, to

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BY MER caror. 1st. ‘Extend from Merid. Diff. of Lat. 1077, to Diff. of Longitude 1192 on the Line of Numbers, that Extent will reach from Radius or 45°, to the Course 47°54', on the Line of Tangents.” 2dly. ‘Extend from Radius or 90°, to the Comp. of 42°6’ on the Line of Sines, that Extent will reach from the Prop. Diff. of Lat. 777, to the Dist. 1159, on the Line of Numbers.”

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... half is 216,2, this multiplied by 4, because the Differelice of Lon

gitude was divided by 4, gives 864=8 the Departure: Again, taking # of the Difference of Latitude, aid : of the Departure 194.2 and 214,2, the nearest Numbers to these standing together are 216.2

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BY MERC AT of.

1st. Look for the Meridian Difference of Latitude and Difference of Long. until they are found standing in their respective Courses, $. if they were Latitude and Departure,) and the Course will be ound among the Degrees or Points in the Latitude Columns; belonging to this; find the Proper Difference of Latitude, opposite to which stands the Dist. in its Column. - -

Now is of the Meridian Difference of Latitude, and the , , of the Difference of Longitude are 170,7 and i 19,2, the nearest Numbers in the Tables are 107,7 and 11 9.6 standing together over 48°, which is the Course; over 48° in the Latitude Column, I look for the , , of the Prop. Difference of Latitude, which is 77,7, the nearest is 77,6, against this stands 116 in the Distance Column, this multiplied by 13 gives 1160 the Distance nearly as before.

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Draw the Meridian AP, make it equal to 855 the Difference of Latitude; on Pere&t the Perpendicular PN, and make it=564 the Departure; join D and N, then will the Angle PDN be the Course N. 33° 25' W. and D N the Distance 1925 Miles.

A, the Distance of the Departure 564, draw E F parallel to D P: with the Chord of 60° describe the Arch T S, and upon it set off the Comp. of the Middle Latitude 45°53' from S to T, through T draw. Dö, to cut E F in O, then will OD be the Difference of Lon. 785,6 Miles, by Middle Latitude Sailing.

- Again Again, produce DP to A, and make D A = 12.o.o the Merid. Difference of Latitude; draw A B parallel to PN, and produce D N until it cuts A B in B; then will A B be 791,7 Miles, the Diff. of Long. by Mercator's Sailing. “Or, the Extent srom the Diff. of Lat. 855, to the Departure 564, will reach from the Meridional Diff. of sat. 1200, to 792, on the

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As the Diff of Lat. 855 2.93.197 As Radius 90° IO.OOOCO Is to Radius 90° 10.coooo Is to the Diff of Lat. 85; 2.931.97

Line of Tangents.’

So is the Departure 564 2.7.5128

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2dly. ‘Extend from Radius or 90°, to the Course 33° 25' on the Line of Sines, that Extent will reach from thc Departure 564, to the Distance 1025, on the Line of Numbers.'

3dly. ‘Extend from Radius or 90°, to the Complement of Middle Latitude 55°53' on the Line of Sines, that Extent will reach from

the Departure 564, to Middle Latitude Sailing.”

785 Miles, the Difference of Longitude by

4thly. ‘Extend from thc Sine of the Course 33° 25' to the CoSine of the Course 56° 35' on the Line of Sines, that Extent will reach from the Meridional Diff. of Lat. 1200 to 792 Miles the Diff. of

Long. by Mercator.”

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Line of Numbers.”

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With the Difference of Latitude and Departure, find the Course and Distance as in Case V.I. in Plane Sailing. Take the Comp. of Middle Latitude as a Course, and the Departure in its Column, the corresponding Distance will be the Difference of Longitude; by Middle Latitude Sailing. And Having found the Course, instead of the Proper Difference of Latitude, find the Meridional Difference of Latitude in the Latitude Column belonging to the Course; the corresponding Departure will be the Difference of Longitude, by Mercator’s Sailing. Now taking to of the Diff. of Lat. '... of the Departure viz. 85.5 and 56.4, the nearest Numbers standing together in the Tables to these are, 85.5 and 55.5, under 33° against Distance 102, and 85.4 and 57.6, under 34° against Distance Iog, now 33° added to 34° is 67, half is 33° 30' the Course; and 102 added to jog gives 205, half is 102.5, which multiplied by Io, gives 1025 the Distance. - To find the Difference of Longitude. Over the Complement of Middle Latitude 46°, find ; of the De

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tance Column, this multiplied by 4, gives 784 Miles, the Diff. of Longitude, by Middle Latitude Sailing.

Again, the Course being 33° 25' or nearly 33° #, look for 1% of the Meridional Diff. of Lat. = 120 in the Latitude Columns, under 33” and 34°, the nearest Numbers to these are 11 c.9 and 120.2, the Departures corresponding are 77.9 and 81. 1, their Sum is 159, half is 79.5, which, multiplied by Io, gives 795 the Diff. of Lon. by Mercator’s Sailing, nearly as before.

From what has been said, it is easy to perceive that all the Cases (save the first) in Middle Latitude and Mercator’s Sailing, are projected and worked in the same Manner as in Plane Sailing, and to obtain the Difference of Longitude by Middle Latitude Sailing, the Complement of the Middle Latitude is taken as the Course in Plane Sailing, and with this Course and the Departure, the Distance is found, which, will be the Difference of Longitude by Middle Latitude Sailing. And having the Course, take the Meridional Difference of Latitude, as if it was the Proper Difference of Latitude, the corresponding Departure will be the Difference of Longitude by Mercator’s Sailing.

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Now 849.8, or 850 divided by 60, gives 14° 10'S. and being subtracted from the Latitude of Cape Ckar, leaves 37° 5' the Latitude in ; Hence the Middle Latitude is found to be 44° 10', and Meridional Difference of Latitude 1194. Whence,

To find the Difference of Long, by
Mid. Lat. Sailing.
As Co-fi. Mid. Lat. 44° 10' 9.8; 57.1
Is to the Departure 567.8 2.75420
So is Radius 90° loooooo

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in

Lat. 51° 15' Merid. Parts 3:03

Lat. 37 co Merid. Parts 2393

Diff. 14 15 = 85; Miles 1 zoo - Merid. Diff. of Lat. Sum 4)88 15-44.7 Mid. Lat.

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