{%G NAVIGATION. 
impreffed on it, whofe diameter was equal to the globe’s 
diameter. The equator being thus confined, the parts 
towards the poles mutt be extended, both in latitude and 
longitude, to fill up the cylinder, or figure in the form of 
a rolling-ftone, and impref’s on its concave furface the lines 
drawn on the furface of the globe. This cylinder, being 
cut on one of the meridians, from north to fouth, and 
laid open, would reprefent a true fea-chart, the parts of 
•which bear the fame proportion to one another as the 
correfponding parts of the globe do ; and on which all the 
lines will be right lines; having every parallel of latitude 
on the globe increafed till it is equal to the equator; and 
fo the diftance of the meridians in thefe parallels will be¬ 
come equal to their diftance at the equator; confequently, 
the meridians on the chart are expreffed by parallel right 
lines. Alfo the meridians being lengthened as the paral¬ 
lels are increafed, every degree of latitude is lengthened 
in the fame proportion as the degrees of longitude are in¬ 
creafed ; therefore, the diftance of the parallels of lati¬ 
tude grows wider and wider as they approach the poles. 
See the article Geography, Plate IV. 
In 1599, Wright published the Principles of the True 
Sea-Chart, and how to conftruft it on the following prin¬ 
ciples : viz. That the diftance between any two meri¬ 
dians at the equator is in proportion to their diftance in 
any parallel of latitude, as the radius is to the cofine of 
that latitude ; that any part of a parallel of latitude is to 
a like part of the meridian as the radius is to the fecant 
of that parallel; and, that the diftance of any parallel of 
latitude from the equator is equal to the fum of the fecants 
of all the arches between the equator and that parallel._ 
From thefe principles, Mr. Wright fet about forming 
a Table, by the continual additions of fecants, of all the 
parallels of latitude, beginning with one minute, which 
he made radius, and thereto adding the fecond parallel 
of 2 minutes, and to the fum of thefe two the fecant of 
3 minutes, &c. The Table thus formed is that which is 
commonly called the Table of Meridional Parts, by means 
of which a true nautical chart may be conftruft.ed, called 
Mercator’s Chart, and all the cafes in Wright's, commonly 
called Mercator’s Sailing, conftrufted and calculated. 
As this Table (fee Moore’s Praft. Nav- Tab. VI.) con¬ 
tains the meridional parts forevery degree'and minute of 
the quadrant, from the equator to the poles, it will be 
eafy to find the meridional parts correfponding to any 
parallel of latitude. 
Ex. Required the meridional parts correfponding to 
the latitude 33 0 45'?—Look in the top of the Table for 
33 0 , and in the right or left hand columns, under the 
degree 33, and oppofite the minute 45, ftands 2153, the 
meridional parts belonging to 33 0 43'. 
When the given latitudes are both north or both fouth, 
the meridional difference of latitude is found by lubtradt- 
Ing the meridional parts of the lefs latitude from thofe of 
the greater. 
Ex. 2. Required the meridional difference of latitude 
between the Lizard, in latitude 49 0 57' N. and the Kland 
of St. Mary’s, in latitude 36° 38' N.? 
The Lizard’s latitude 49 0 57' N. Meridional parts 3470 
St. Mary’s latitude 36 58 N. Meridional parts 2390 
Meridional difference of latitude 1080 
When the latitudes are one north and the other fouth, 
the meridional difference of latitude is found by adding 
the meridional parts correfponding to both the latitudes 
together. . 
Ex. 3. Required the meridional difference of latitude 
between Cape Verd, in latitude 14 0 46' N. and the Cape 
of Good Hope, in latitude 34 0 29' S. 
Cape Verd’s latitude 14 0 46'N. Meridional parts 896 
Cape of Good Hope’s 34 29 S. Meridional parts 2207 
Meridional difference oflatitude 3103 
The feveral cafes in Mercator’s failing are worked by 
geometry, trigonometry, Gunter’s fcale, and the Tables 
of Difference of Latitude and Departure, exaftly in the 
fame manner as thofe in plane failing, by only confider- 
ing the meridional difference of latitude as if it were the 
proper difference of latitude, and the difference of longi¬ 
tude as the departure; for it is no more than enlarging 
the proper difference of latitude, fo as to be equal to the 
meridional difference oflatitude ; then will the difference 
of longitude bear the fame proportion to the departure, 
that the meridional difference of latitude does to the 
proper difference of latitude; for, in figure 7, (which 
is the firft cafe in Mercator’s failing,) let MT reprefent 
the meridional, and M L the proper difference of latitude, 
T H the difference of longitude, LO the departure, MO 
the diftance, and the angle T M H, or L M O, the courfe; 
then willMLbe in proportion to L O, asMT is toTH; 
and the contrary. 
Wherefore, as the proper difference of latitude is to 
the departure, fo is the meridional difference of latitude 
to the difference of longitude ; and as the meridional dif¬ 
ference of latitude is to the difference of longitude, fo is 
the proper difference oflatitude td the departure. 
Since lengthening or fhortening the tides of a triangle 
does not alter the angles, the departure may be reduced 
into difference of longitude, and the difference of longi¬ 
tude into departure. 
In all the cafes (fave the firft) in Mercator’s failing, 
the courfe, diftance, difference oflatitude, and departure, 
are found in the fame manner as thofe in plane failing ; 
and then the difference of longitude may be found by ei¬ 
ther of the following proportions, viz. 
By making the enlarged Diftance M H radius, it will be 
As the coline of the courfe 
is to the merid. diff. oflatitude. 
So is the fine of the courfe 
to the difference of longitude ; 
Or, 
By making meridional Difference of Lat. M T radius, it 
w ill be 
As radius 
is to the merid. diff. oflatitude, 
So is the tangent of the courfe 
to the difference of longitude. 
But in the firft Cafe, it will be 
As the merid. diff. of lat. MT 
is to radius 
So is the diff. of longitude T FI 
to the tangent of the courfe ; 
And 
As radius 
is to the proper diff - . of lat. M L, 
So is the fecant of the courfe 
to the diftance MO. 
Or, when the courfe is found, you may fay, As the co¬ 
fine of courfe is to the proper difference of latitude, fo is 
radius to the diftance. 
Prob. The latitudes and longitudes of two places given, 
to find the dire <51 courfe and diftance between them. 
Ex. Required the bearing and diftance between the 
Lizard, in latitude 49 0 57' N. longitude 5 0 12' W. and the 
I (land of St. Mary, one of the Weftern Iflands, in lati¬ 
tude 36° 58' N. and Ion. 25 0 12' W. 
Liz. lat. 49 0 57' N. Meridional parts 3470 Ion. 5 0 12' W. 
St.Mary’s36 38 N. Meridional parts 2 390 Ion. 25 12 W. 
Dif.oflat. 12 59=2779 Mer. dif. lat. 1080 dif.2o - ooi=i2oo 
60 60 
* 779 miles Diff. Ion. 1200 miles. 
By Projection .—In the fame fig. 7. draw the meridional 
MT=io8o, the mer. difference of lat. and MD22779, the 
proper difference of lat. perp. to MT, draw TH and LO ; 
make 
