MAP, 
103 
$0, and the point 80 in the equator, or dia- 
meter AB ; describe a circle to pass through 
the three given points as follows: with the 
radius 90 set one foot of the compasses on 
the point 90, and describe the semicircles 
XX and ZZ, then remove Hie compasses to 
the point 80 on the equator, and describe 
the arcs 1, 1, and 2, 2 ; where they intersect 
the semicircle make the point, as at 1 and 2, 
and draw lines from 2 through the point 1 till 
they intersect the diameter BA continued in 
E : then will E be the centre from whence 
the meridian 90, 80, 90, must be drawn, and 
will express the meridian of 80° W. longitude 
from Greenwich; the same radius will draw 
the meridian expressing 1 40° W. longitude, 
in like manner : draw the next meridian with 
the radius CB, set one foot of the compasses 
in the point d, and describe the arcs a a and 
bb, then draw lines as before, which will give 
the point D, the centre of 90° W. longitude; 
so of all the rest. 
The parallels of latitude are drawn in the 
same manner, with this difference, that the 
semicircles XX and ZZ must be drawn from 
the points A and B, the extremities of the 
equator. 
In the manner above described, with great 
labour and exactness, Mr. Ar owsmith, to 
whom we are indebted for a part of this ar- 
ticle, drew all the meridians and parallels of 
latitude to every degree on two hemispheres, 
which laid the foundation of his excellent map 
of the world. 
We shall now proceed to shew how the 
same thing may be done mechanically, both 
with regard to the globular and stereographic 
projection. 
( 1 ) The Globular Projection of the Sphere on the Plane 
of a Meridian. 
Draw the circle WNES, fin; 3, draw the two 
diameters NS and WE at right angles with each 
other. 
Divide the arc of each quadrant into nine 
equal parts. 
Divide the radii also in the same manner into 
ninety equal parts each. 
The diameter NS is the meridian, and the dia- 
meter WE is the equator. 
The other meridians are arcs of circles, for 
each of which, as we have seen, there are three 
given points through which it must pass, and 
those are the two poles NS, and a division on 
the semi-diameter WC, viz. either a, b, c, d, e, f 
g, or h. The centres for these arcs will be in 
the line CE produced ; and the centres for those 
on the other side, will be oh the fine CW pro- 
duced. 
For the arc SaN. the radius 
— SAN. — 
— Sc N. — 
— SafN. — 
— S?N. — 
— S/N, ~ 
_ SgN. — 
— SAN. — 
an— 90,6 1 ") 'S S 
bb — 92,82 
cc — 97,32 £ fi 
dd — 106 o> 
ee — 121,1 
ff— 149,7 
gg — 215,6 
hh — 410,7 Jo & 
And for each of the arcs representing the pa- 
rallels of lat also there are threegiven points ; viz. 
one of the divisions l, l m, a, o , p , q, or r , upon 
the meridian SN, and the two corresponding 
divisions of the circumference. The centres for 
these arcs will fall on the line 3N, produced 
both ways, and the following table shews the 
length of the radius of each equal part, in equa- 
torial degrees, as in tire former case. 
4 
For the arc 
80 r 80 the radius rr — 
70 q 70 
665 A. 665 
77 . : 
A. Arctic : 
60 p 60 
50 o 50 
40 n 40 
30 7n 30 
23| T. 23-*- 
20 / 20 " 
10 k 10 
18,44 
39.75 
48,19 
— pp — 65 ,3 
— 07 — 97,71 
— nn — 143 
— mm 210 
— T. Tropic — 281,4 
— II = 337,5 
• — - lb ~ 703,5 
rt.3 
(2) The Stcreographic Projection of the Sphere on the 
Plane of a Meridian. 
Draw a circle NF.SW, fig. 4, and the two dia- 
meters of it at right angles with each other. 
Divide the arc of each quadrant into nine 
equal parts. 
From the point E, draw dotted lines to each 
point of division on the arc WN. 
The intersections made by this means on the 
semidiameter CN, mark a line of semitangents, 
which must also be set off on the other three 
semi diameters, CS, CW and CE. 
Draw likewise two dotted lines from E to 23§° 
and 66-*;° for the tropic and polar arcs, which 
must also be set off on the semi-diameter CS. 
Each point of intersection on CN, an 1 the 
corresponding divisions on the arcs WN and j 
EN,are the three points Trough which the arcs 
of latitude must pass ; and their centres will be 
in the line NS produced. 
Take the radius of the same circle for a scale; 
divide it into nine equal parts, and each of those 
parts into ten other parts, as before 
Tiie following table exhibits the length in 
those parts of the rad-us, which must be taken 
to describe each respective arc. 
For the arc 
80 
r 
80 
the radius rr 
— 13,87 A 
70 
s 
70 
SS 
~ 32,75 
W O 
C/5 CJ 
66i 
A 
665 
— A. Arctic 
— 39,19 
rt p 
60 
t 
60 ‘ 
— It 
= 51,96 
50 
*v 
50 
— w 
= 75,52 
40 
IV 
40 
IV 7 V 
= 107,3 ’ 
P A> 
rTJZ 
30 
X 
30 
— XX 
= 155,9 
V *-> 
d 
23i 
T. 
235 
— T. Tropic 
= 207 
O *-P 
20 
y 
20' 
— yy 
— 247,3 
• p 
10 
z 
10 
— ZZ 
= 510,4 
.0 * 
The 
two polar points N, S 
and the 
semitan- 
gents on CE, mark the three given points 
through which each meridian line must pass. 
The following table exhibits the length of 
each radius to describe the meridian arcs. 
For the arc NsS. the radius aa — 91 ,4 (~'o 3 
NAS 
NTS. 
NVS. 
NrS. 
N/S. 
NT. 
NTS. 
bb — 95,78 
cc — 104 I rt 2 
dd— 117,5 
ee — 140 1 II ~ S 
ff— ISO j_2'5’5 
hh ■=. 513,3 [_Q £ u 
(3) The Globular Projection of the Sphere on the Plane 
of the Equator. 
On the centre P, fig. 5, draw the circle WN 
ES, to represent the. equator. 
Draw the two diameters, WE and NS, at 
right angles with each other. 
Divide the arcs of the four quadrants into 
nine equal parts ; each of the parts will be equal 
to ten degrees. 
Number them from N towards P, 10, 20, 30, 
40, 50, See. 
On the centre P draw circles passing through 
those points of division, which will be the cir- 
cles of latitude. 
For the arctic circle, set off 23^° from # P to- 
wards N ; do the same at N towards P, for the 
tropic circle. 
Through each of those points draw an ob- 
scure circle. 
Draw diameters from the divisions on one 
half of the circumference to the corresponding 
divisions on the opposite or.e. to represent the 
meridians, and this will complete the projection, 
(4) The Stereographic Projection of tic Sphere on the 
Plane of the Equator. 
Draw the circle N,W, S, E.fig. 6, and the two 
diameters at right angles with each other. 
Divide the arcs of each of the four quadrants 
into nine equal parts ; subdivide each of those 
parts into 10 degrees ; number those degrees 10, 
20, 30, See. 
Draw diameters from the divisions on one side 
of the circumference to the corresponding divi- 
sions on the other, which will represent the me- 
ridians. 
For the parallels of latitude, project a line of 
semitangents as directed in the 2d case. 
On the centre P describe circles passing 
through the semitangents, which will complete 
the diagram. 
Note. The foregoing methods of projecting 
the sphere are the best. There is another me- 
thod sometimes used, viz. the projection on the 
plane of the horizon when any assumed place 
is considered as the centre ; but as this method 
is rarely used, it need not he elucidated. 
3 he orthographic projection is in fact so er- 
roneous, that it ought to be entirely rejected for 
that purpose, and applied only to dialling. 
J lie gnomonical projection is only applicable 
to dialling. 
We shall now point out the advantage and 
disadvantage of Mercator’s projection. 
A method has been found to obviate some 
of the difficulties attending all the circular 
projections by one, which, from the person 
who first used it (though not the inventor), is 
called Mercator’s projection. lu this there 
are none but right lines : all the meridians are 
equidistant, and continue so through the 
whole extent; but, on the other hand, in or- 
der to obtain the true bearing, so that the 
compass may be applied to the map (or 
chart) for the purpose of navigation, the 
spaces between the parallels of latitudes 
(which in truth are equal, or nearly so) are 
made to increase as they recede from the 
equator in a proportion which, in the high la- 
titudes, becomes prodigiously great. 
The great advantages peculiar to this pro- 
jection are, that every place drawn upon it 
retains its true bearing with respect to alt 
other places ; the distances may be measured 
with the nicest exactness by proper scales, 
and all the lines drawn upon it are right lines: 
for these reasons it is the only projection in 
drawing maps or charts for the use of naviga- 
tors. We shall shew the method of this kind 
of projection. 
Mercator's or JPriphCs projection of 
? naps . — Draw the line AB, tig. 7, and divide 
it intc as many degrees as your map is to 
contain in longitude, suppose 90°. At the 
extremities A and B raise perpendiculars, to 
which draw parallel lines a^every single, fifth, 
or tenth degree of the equator, for the meri- 
dians ; as in the figure, where they are drawn 
at every tenth degree. Tuis done, put one 
foot of the compasses in the point A, and ex- 
tending the other to the point in the first me- 
ridian in the equator G; or, for greater ex-- 
actness, to some more distant point, as B 90 ; 
describe the quadrant F.' : , winch divide into 
nine equal parts, and draw n lines from A to ■ 
each point of the division; or, to avoid scor- 
ing the paper, only mark where a ruler cuts 
the first meridian GH, at every tenth degree’s - 
distance. Lastly, because the distances of 
the parallels ft cm -one another are marked^. 
