625 
NAVIGATION. 
Hence it follow^, that. 
As radius, or fine 90 0 
is to the diff of Ion. in miles. 
So is cofine of any para!, of lat. 
to the dift. in miles between any two mer. in that paral. 
of lat. And, 
As cofine of any paral. of lat. 
is to the diftance run in miles in that lat. 
So is the radius, or fine of 90 0 
to the diff. of Ion. in miles. 
Prob. The difference of longitude between two places, 
both in one parallel of latitude, being given, to find the 
diftance between them. 
Ex. Suppofe a (hip in the lat. 49 0 30' N. or S. fails di- 
redlly E. or W. until her diff. of Ion. be 3 0 30', and the 
diftance failed be required. 
As rad. 90 0 - - io-coooo 
is to the diff. of Ion. 210 - 2.32222 
So is cofine lat. 4.9 0 30' - 9-81254. 
to the dift. or dep. 136 4. 2-13476 
By the reverfe of the laft Problem, Having the dift. 
run in any parallel to find the diff. of Ion. 
Ex. Suppofe a (hip in lat. 49 0 30' N. or S. fails diredlly 
E. or W. 136-4 miles, and her dift'. of Ion. be required. 
As cofine of lat. 49 0 30' co.ar. 0-18746 
is to the dift. 136-4 - - 2-13481 
So is rad. - - - io'ooooo 
to the diff. of Ion. 210 - 2-32227 
In the laft Problem, the ftiio is fuppofed to have failed 
due eaft or weft, in the fame parailel of lat. but in her 
courfe fhe generally c roffes feveral meridians and parallels, 
and then arrives at a different lat. from that (he left; and, 
as it is plain, by the foregoing Table, that the miles 
which make a degree in one parallel will not be the fame 
as thole that make a degree in any other parallel, lying 
on the fame fide of the equator, therefore add both lats. 
together, and take half their fum for a mean or mid. lat. 
which may be conceived as if the ftiip had failed in one 
lat. with which the diff. of Ion. may be turned into dep. 
and dep. into diff of Ion. in the fame manner as has been 
already fttown ; for it will be. 
As radius 
is to the difference of longitude. 
So is the cofine of the mid. lat. 
to the departure. 
And, 
As the cofine of the mid. lat. 
is to the departure, 
So is radius 
to the difference of longitude. 
Ex. Required the bearing and dift. between the Lizard, 
in lat. 49 0 57' N. Ion. 5 0 12' W. and the Ifland of St. Mary, 
one of the Weftern Illands, in lat. 36° 51'N. and Ion. 
2 5 0 12' W. 
Lizard’s lat. 49 0 57'N. 49 0 57' Ion. 5°i2'W. 
St. Mary’s lat. 36 58 N. 36. 58 Ion. 25 12 W. 
12 59 Sum 2)86 55 20 o 
60 - 60 
•-- Mid. lat. 43 28 --- 
Diff. in miles 779 90 00 i2oodiff.lon. 
Co-mid. lat. 46 32 
By Projection. 
In fig. 6. draw the mer. A E, with the chord of 60 de- 
fcribe the arch PS; upon which fet off 46° 32', the comp, 
of mid. lat. from Q to S; through S draw the line AC=i 200, 
the diff. of Ion. let fall the perpendicular CE, which will 
be the dep. 870-9 ; upon A E fet off A D 779, the diff. of 
lat. and upon D ereft the perp. DG, and upon it fet oft' 
Vol. XVI. No. 1141. 
the dep. 870-9. Then join G and A, and it is done ; for 
G A will be the dift. 1168 miles, and the angle GAD the 
cou. S. 48° 4' W. 
By Calculation. 
To find the Departure. 
As radius - - - 
is to diff. of Ion. 1200 
So is cofine mid. lat. 43 0 28' 
IO'OOOOO 
307918 
9-86080 
to the dep. 870-9 - 
2-93998 
To find the Courfe. 
As diff of lat. 779 co. ar. 
is to the radius tan. 45 0 
So is dep. 870 9 - 
7*10846 
10*00000 
2-93998 
to tang, of cou. 48° 11' 
10-04844 
Note. The courfe may be found without the departure, 
by middle-latitude failing, thus : 
As the dift’. of lat. 779 co. ar. 7-1084.6 
is to the diff Ion. 1200 - 3-07918 
So is cofine mid. lat. 43 0 28' - 9-86080 
to tang. cou. 43 0 11' 
10-04844 
To find the Diftance. 
As fine cou. 48° 11'co. ar. 
is to dep. 870-9 
So is radius 90 0 
0-12768 
2-93998 
10*00000 
to the dift. 1168 
3-06766 
Of MERCATOR’S SAILING. 
Plane failing, as has been before o'oferved, fuppofesthe 
earth and lea to be in the form of a bowling-green, on 
which the meridians are parallel, and the degrees of lati¬ 
tude and longitude equal in all places; but the earth and 
fea compofe a round body, or globe, on which the de¬ 
grees of latitude are equal in all places, and the degrees 
of longitude decreafe from the equator in proportion to 
the fine-complements of the latitude. 
Though the meridians all meet at the poles, and the 
parallels to the equator continually decreale, and that 
in proportion to the cofines of their latitudes, yet in old 
fea-charts the meridians were drawn parallel to each other, 
and, confequently, the parallels of the iatitude made 
equal to the equator, and fo a degree of longitude on any 
parallel as large as a degree on the equator ; alfo, in thefe 
charts, the degrees of latitude were ftill reprefented (as 
they are in themfelves) equal to each other, and to thofe 
of the equator ; by thefe means the degrees of longitude 
being increafed beyond their juft proportion, and the 
more fo the nearer they approached the poles, the degrees 
of latitude at the fame time remaining the fame; it is 
evident places mull: be very erroneoufly marked down 
upon thofe charts, with refpeft to their latitude and lon¬ 
gitude, and confequently their bearings from one an¬ 
other muft be very falfe. 
To remedy this inconvenience, fo as Hill to keep the 
meridians parallel, it is plain we muft lengthen the de¬ 
grees of latitude in the fame proportion as thole of longi¬ 
tude are, that fo the proportion in eafting or welting may 
be the fame with that of northing or fouthing ; and, con¬ 
fequently, the bearing of places from each other to be the 
fame upon the chart as upon the globe itfelf. 
The difficulty in conftru&ing a true fea-chart Confifts 
in finding a proper manner of applying the lurface of a 
globe to a plane; which Mr. Wright, an Englilhman, by 
an ingenious improvement and application of what was 
called Mercator's Chart , happily accomplilhed. He con¬ 
ceived the furface of this globe to fweil like a bladder 
while it is blowing up from the equator towards the poles, 
proportionally in latitude as it does in longitude, until 
eyery part of its furface meets that of a concaye cylinder 
7 U impreffecL 
