latitudes of the different parallels, deducting radius from 
each; that is, C 20 (Fig. 4.) reckoning from C towards 
N, is the log. ate or 35°, = log. tan. 55°; 
C40 = log. cot. ase or 25°, = log. tan. 65°, &c. 
always deducting radius. Advantage has accordingly 
been taken of this principle, by adapting a line of such 
nts to the eonstruction of charts. . This line is to 
be found-on the common Gunter’s scale, adjacent to the 
line Mer. and marked Tan. Like the former, it com- 
mences on the right hand, and is constructed on the fol- 
lowing principle. 
_ As radius is to be deducted from each tangent, before 
of ing it tothe scale, and as all tangents below 
ithmie 45° are less than the radius, none ‘less than that of 45° 
ts. can be exhibited on the line. Nor, 
tangent necessary, as half the colatitude never can be 
greater, or, which is the same thing, the complement 
of half the colatitude, never can be less than 45°. From 
the extremity of the line, therefore, which is marked 
45°, rithmic tangents of all the arches ter 
than 45°, auleuing radius, are set off towards the left 
~ hand, and numbered at every tenth division, 50, 60, 
70, &c. But the logarithmic tangent of any arch, as 
yO es 1O 
50° = log. cot. 90° — 50° or 40°=log. cot. —— Bs 
log. cot. of half the colatitude of 10°. In like manner, 
ala = cot. of half the 
colatitude of 20°, and so of others. To facilitate, there- 
fore, the application of the line, the divisions marked 
50, 60, 70, &c. are also numbered 40, 30, 20, &c. by 
which means they exhibit at once the half colatitudes, 
to which the tangents 50, 60, 70, &c. are cotangents. 
Hence the following simple rule, for finding the pro- 
jected distance of any parallel of latitude, from the 
equator. 
Extend the compasses from the extremity of the line 
45, to the number denoting half the colatitude of the 
parallel, and it will be the distance required. Thus, 
the distance of the parallel of 20° is found by extending 
the compasses from 45 oo = 35, and so of any 
of the 
tan. 55° = cot. 35° = cot. 
~ Se ceeee re 
tween any two parallels, take the distance between the 
numbers denoting half the colatitudes of each; thus 
the distance between the parallels of 20° and 40° on 
= chart =the distance between 35 and 25 on the 
le. 
But though the distances of the parallels, or the len 
of the oe of latitude, are thus readily found, it is 
obvious that these distances must correspond to some 
particular scale of longitudes. In order, therefore, to 
construct a chart by the line of tangents, it becomes ne- 
cessary to determine the ge ei of the degree of longi- 
tude which corresponds to that line, and which iday he 
found thus, 
o. Take from the line Mer. any latitude whatever, as 
Jon. 27° 6’, and applying that distance to the line E: P, 
mark the corresponding length, which in this case will 
be 40; or divide the number oppesite to 87° 6’ in the 
table of meridional parts, which is 2400, by 60, and 
mark the quotient, viz. 40, From 45 on the line Tan. 
extend the compasses to half the colatitude of 37° 6’, the 
assumed latitude, which is 26° 27’ ; apply this distance 
to any scale of equal parts, as of 1 ioe and divide the 
corresponding distance, which in this case will be about 
VOL. X. PART T. 
tell, wer oe 
GEOGRAPHY. 
indeed; is any less: 
other. Hence also, to find the projected distance be- 
169 
3.4 in, by 40, the number found on E: P, or from the Matliemeri. 
table corresponding to the assumed latitude ; the quo- + aa 
tient, in the present instance .085, will be the length wire 
of a degree of longitude, corresponding to the above la~ 
titudes, in terms of the unit of the seale of equal parts, 
viz. inches. Hence, if the distances of every tenth pa- 
rallel be taken from a line of tangents of the dimension 
supposed above, every tenth meridian will be found by 
setting off on the equator, or on any parallel of latitude, 
divisions each equal to .85 in. 
It follows, from the meridians in this projection being 
parallel to one another, that the rhumb-lines, which on 
the globe are spirals continually approaching the poles, 
are represented on the chart by straight lines ; a pro- 
perty, which renders this construction of vast import- 
ance in navigation, See Navication. 
. The only. other projection that we shall notice, as Construc- 
connected with the subject of the present Section, is tionof gores 
the construction of gores, for covering globes, each of ae 
which may be considered as a developement of a small § 
portion of the surface of the sphere, extending longi- 
tudinally, in the direction of the meridian. We for- 
merly observed, in treating of’ the construction of globes, 
that in an indefinitely small portion of the sphere, 
ZENQS (PlateCCLXV. Fig.7.), EQ and ac, portions of FEAT. 
the equator and a parallel of latitude, may be regarded Fig. wo. 
as straight lines, perpendicular to MN. In practice, 
however, the gore is not taken so small as to warrant 
this assumption; and therefore these lines are really 
portions of circles. The following method of project- 
ing gores, has been recommended by several eminent 
artists, as well as astronomers. 
Draw a straight line EQ, equal to the breadth of the 
intended gore at the equator, which is generally +, 
of the whole circumference, and bisect it by a perpen 
dicular MN, equal to } of the circumference. Divide 
MN into 9 equal parts, and through each, from points 
in MN produced, with radii equal to the cotangents of 
their respective latitudes, to rad. MN, describe arches for 
the parallels of ‘every 10th degree. From each of the 
divisions in MN, and with radii equal to the fractions 
opposite their respective latitudes in the Table, p. 151, 
multiplied into the length of MS, describe es in- 
tersecting the parallels, on both sides of MN; then the 
curves Na H, NcQ drawn through these. divisions, 
will be the meridians distant from one another 4, of 
the circumference, or 30°, that is the segment of the 
gore ZE.aN ¢ Q applied to the globe will cover 4, of a 
misphere. The same operation repeated will give 
the a gores, after which the different portions of 
the earth’s surface, or celestial sphere, are to be delinea« 
ted as on any other maps. , The globe, as'was formerly 
observed, is generally covered im this way, from the 
equator to the parallel of 70° or 80°; but the space 
round the pole is projected on one cireular piece, whose 
radius is equal to the sine of its distance from the pole» 
It is hardly necessary to observe, that neither by, this, 
nor any other method, can gores be constructed, so as 
accurately to cover any given, portion of a sphere. It 
is even found that the dimensions of the different 
pieces, undergo a considerable alteration in consequence 
of their being moistened, for the purpose of being fixed 
on the globe. The best method of correcting these ir- 
regularities, is by enlarging or diminishing, as may be 
necessary, the size of the globe itself. 
Sect. IV.. Construction of Maps representing small 
Portions of the Earth’s Surface, and the Method of 
filling up the Outlines of Maps in general. 
Tuouex the various methods of projection, explain- 
ed in the course of this article, are sufficient for the con- 
¥ 
