GEOGRAPHY. 365 
map, are truly exiiibited ; and of conrfe equal fpaces on 
the earth, or on the globe, are reprefented by unequal 
fpaces on the map ; a defeft propofed to be remedied 
by the globular projedlion. 
But if, inltead of its globular figure, vve' fuppofe the 
earth to have a conical form, it is plain, that tlie meri¬ 
dians would be reprefented by llr.iight lines diverging 
from the apex of the cone, while tiie parallels are fhown 
by concentric circles placed at equal diftances. This 
kind of projection is not without its ufe. It hath this 
great advantage, that the longitudes and latitudes may 
be found with the greateft eafe by means of a moveable 
index placed on the centre. The whole earth may alfo 
be thus reprefented on a fingle circle : but thus the 
countries towards the fouth pole are prodigioufly aug¬ 
mented in breadth in proportion to their length ; for 
the degrees of longitude conftantly incrcafe the farther 
we are removed from the pole, wliile thofe of latitude 
flill remain the fame. This apparent error, however, 
doth not in the leafi: affedt the real proprortion of tlie 
map, or render it more difficult to find the longitudes, 
or latitudes upon it; as may be feen by an infpedtion of 
fig. 2, Plate III. 
Mercator’s projeflion fuppofes the earth, infload of a 
globular, to have a cylindrical figure ; in confequence 
of which, the degrees of longitude become of an equal 
length throughout the whole furface, and are marked 
out on the map by parallel lines. The circles of lati¬ 
tude alfo are reprefented by lines croffing the former at 
right angles, but at unequal diftances. Tlie farther we 
remove from the equator, the longer the degrees of la¬ 
titude become in proportion to thofe of longitude, and 
that in no lefs a degree than as the fccant of an arch to 
the radius of the circle: that is, if we make one degree 
of longitude at the equator the radius of a circle ; at 
one degree diftant from the equator, a degree of latitude 
will be exprefled by the fecant of one degree ; at ten 
degrees diftance, by the fecant of ten degrees ; and lb 
on. A map of the world, therefore, cannot be deli¬ 
neated upon this projection, without diftorting the fliape 
of the countries in an extraordinary manner. The pro¬ 
jection itfelf, however, as above noticed, is moft ufeful 
in navigation, fince it ftiews the different bearings with 
perfect accuracy, which cannot be done upon any other 
proje6lion. See Map of the World on Mercator’s pro¬ 
jection, Plate XI. 
The globular projeilion, above recommended and de¬ 
fined, is an invention of M. de la Hire, and is more ufe¬ 
ful than any of the others for exhibiting the true fhape 
of the countries. To this, therefore, we have given the 
preference, except for the purpofes of navigation, where¬ 
in Mercator’s projection is ever to be preferred. 
In moft of thefe projections, the firft meridian is made 
to pafs through Ferro, which is 17° 45' 50*' weft of 
Greenwich. To reduce therefore the longitude from 
Ferro to tliat from Greenwich, add 17° 45' 50" if the 
place be wejl oi Ferro, and it gives the longitude weft 
from Greenwich ; if the place be eajl of Ferro, and in 
longitude lejs than 17° 45' 50", the difference of its Ion- 
gitude and 17° 45' 50" Ihews the longitude weft from 
Greenwich; but if the longitude begreairr than 4.^' ^o", 
the difference fiiews the longitude caft of Greenwich. 
Thus we may reduce the longitude from one place to 
that from any other. 
For mapping elevated lands, or for laying down the 
heights of mountainous and hilly countries, an inge¬ 
nious method of projection has been recently fuggefted 
by Mr. John Churchman, of John-ftreet, Tottenham- 
court, London; and for which the London Society of 
■Arts, in 1804, prefented him with their filver medal. 
We fhall ftate this improvement in his own words; 
“ It appears to be a matter of much importance to 
the people of any country, at all times, whether in war 
®r peace, to poffefs a complete knowledge of its furface. 
in war, fuch knowledge is abfolutely neceli'ary for de. 
. VoL, VIII. No. 509. 
•fence; in peace, for improving the country to the beft 
advantage. Now, llnce geograpliy may be improved, 
an eafyand accurate method to lay down maps of moun¬ 
tainous countries and hilly eftates, will perhaps prove 
ufeful, as it will fhew at a fingle view the true fliape and 
comparative height of the ground without the art of 
painting. 
' “ As mountains are apt to eclipfe each other, a per- 
fpediive view is feldom very extenfive, the rules of 
which fall fliort of giving an accurate idea of any hilly 
country ; becaufe fuch a view, though ftridtly true in 
one particular place, is not fo in any other. The alti¬ 
tudes of mountains appear in proportion to the diftance 
from the eye, and no rule in geometry has been found 
fufticient to determine diftances, from any fingle ftation. 
Neither can a bird’s-eye view of an eftate afeertain the 
depth of valleys, or the height of mountains. But the 
method here propofed will be found equally capable of 
giving the true fliape of any ground above or below wa¬ 
ter. It may be fticcefsfully applied to fea charts, and 
will prevent much confufion, arifing from the tedious 
method of diftinguiftiing foundings by a multitude of 
figures. 
“ Suppofc a full defeription is -required to be given 
of any ifland in the ocean. Firft, let an accurate map 
be laid down in the common way ; and let the perpen¬ 
dicular height between the higheft point of land and the 
ocean be divided into any number of equal parts. Sup- 
pofe thefe equal divifions are 100, 200, 300, 400 feet 
above the low-water mark. From the dift'erent points 
of thefe feveral divifions, let horizontal lines be run 
with a good theodolite, and fpirit level annexed, all 
round the ifland. If the work is well done, each line 
will end where it began ; and if the bearings and dif¬ 
tances of thefe feveral lines are truly laid down on the 
map, the crooked courfes of them will clearly fhew the 
fhape of the ground over which they pafs. For exam¬ 
ple: if any horizontal line paffes by the fide of a fteep 
hill, it will incline tow'ai'ds the ocean, or approach the 
next horizontal line below it. When the fame line croftes 
a ftream of running water or a valley, it wdll naturally 
bend up the fide of the laid ftream, until it can crofs it 
without lofing the level ; or, in other words, it will 
bend towards the centre of the ifland. Hence, by a 
little praddice, tlie fhape of the feveral horizontal lines 
on the map will give as clear an idea to the mind, of 
the fliape of any country over which they pafs, as a 
fight of the country itfelf can convey to the eye. But 
to obtain a mathematical and true knowledge of the al¬ 
titude and declivity of any part of thecountryj we have 
the following propofition : — 
“As the perpendicular height of any one horizontal 
line above another is to the radius : fo is the horizontal 
diftance between the horizontal lines meafured on the 
map at any particular place, to the co-tangent of de¬ 
clivity at that place.—If the horizontal diftance be. 
tween any two horizontal lines on the map i^ equal to 
the perpendicular height of any horizontal line above 
another, the angle of altitude, or declivity, of any hill, 
will be 45 degrees. 
“ The prefent improvement will be found to pofTefs 
the following advantages :—ill. Military men are well 
acquainted with the many advantages always to be 
gained from the exadl reprefentation of high grounds. 
By this inethod, we are able to give the angle of alti¬ 
tude, the angle of declivity, and perpendicular height, 
of every hill ; likewdfe the comparative height of dift'e- 
rent hills, the beft route by which the high grounds 
may be gradually afeended, and where heavy burthens 
can be drawn up with moft eafe.—2dly. Experience has 
fufficiently fliewn, that the inhabitants of low grounds 
are fubjedl to different kinds of llckncfs, from which 
thofe living at places elevated to a certain degree are 
exempt. A map on this improved plan will point out 
the m«ft proper lituation for building dwelling-houfes. 
5 A n 
