projection 
alent map-projection In which the parallels are repre- 
sented l>v parallel straight linen at distances from the 
equator proportional to the tangents of half the latitude*. 
This projection was proposed In 1862 by M. de Propel It 
Foucaut. t'lanutrnti map-projection. Same u tiniuoid- 
al map-projection. Foucaut i map projection, the equiva- 
lent atercographic map-projection, fournirr'i map-pro- 
jection, (a) A meridional map-projection In which the me- 
ridians are equidistant ellipHes, while the parallels are cU~en- 
lar arcs equally dividing the central and extreme meridians. 
(i>) A map-projection In which the meridians are u In (a\ 
but the parallels are straight lines as in ttie meridional 
orthogonal projection. These map-projections were pro- 
posed In 1646 by t he French geographer Fournler. Gaiuu't 
map-projection. Same as Lagranye't map-projection Ola- 
reantts's map-projection, a discontinuous map projection 
differing (rum that of Apianus only In setting the paral- 
lels at the same distances as in the meridional ortho- 
graphic map-projection. It was Invented by the Swiss 
mathematician Loriti or Ulareaims, and published in 
1527. Globular map projection, (a) Any projection of a 
hemisphere with curvilinear meridians and parallels. ('<) 
A meridional hemispherical map-projection In which the 
equator is a straight line, the senifmeridians are circular 
arcs dividing the equator Into equal parts, and the paral- 
lels are circular arcs dividing the extreme and central me- 
ridians Into equal parts. This projection, Invented in 1660 
by the Italian Mcoloal, has been extensively employed 
ever since. () La Hire's map-projection. Onomoiac map- 
projection, (a) A perspective map projection from the 
center of the sphere. All great circles are represented by 
straight lines. lience, by extension (b) Any map-pro- 
4763 
proportional to log tan i latitude. This has the advantage 
that the point* of the compass preaerve the same direc- 
projector 
n. an equivalent projection which 
Cnoinonic Projection. 
jectlon representing all great circles by straight lines. 
Such a projection can contain but one half of the sphere on 
an Infinite plane. This system Is probably ancient. llitr<l 
ilia's map-projection. Same as Lo.ijra.iuje'* map-projection. 
Uerschets map-projectitm. Same as Lairranjjes map- 
projection. - Homalotrraphic (or homotinjraphic) map-pro- 
jection, an equivalent map-projection in which the meridi- 
ans are ellipses meeting at the poles, and the parallels and 
equator are parallel straight lines: Invented by the Ger- 
man mathematician Mollwelde in 1805. It ha> been con- 
siderably used. Intermediary map-projertion, a zenithal 
map-projection in which, z being the zenith distance of an 
almucantar, r Its radius on the map, and u a constant, 
i- 11 tan : n. 
This projection was Invented by A. Germain. Irreira.- 
lar map projection. Same as duenntiimuut map-projec- 
tion. Isocyfindric map-projection, an equivalent map- pro- 
jection the development of a cylinder upon which the 
sphere has been orthogonally projected. It was invent- 
ed by the German mathematical philosopher J. H. Lam- 
bert. Itomeric map-projection, the zenithal equivalent 
map-projection, invented by J. U. Lambert, and the 
best of the equivalent projections. Isorpherical map- 
projection. Same as Homeric map-projection. Jaeger's 
map-projection, a discontinuous projection In the shape 
of an eight-pointed star. It was proposed by Jaeger 
in 1865, and was modified by Petermann. Jamet's map- 
projection, a perspective map projection In which the cen- 
ter of projection is distant from that of the sphere by 1.5 
times the radius. It was Invented by the English geodesist 
Sir Henry James. Layrana.e'8 map-projection, an ortho- 
morphic map-projection in which the sphere is shown a 
finite number of times on a Unite number of sheets, but in 
which all the north poles (or zeniths) coincide, as well as 
all the south poles (or nadirs). ' '"' projection was in- 
vented by J. II. Lambert, and has been called by many 
names. It has been used in a government map of Russia. 
La Hire's map-projection, a perspective projection hav- 
ing the center of projection at a distance from the center of 
the sphere equal to 1.707 times the radius. This projec- 
tion, proposed by the French geodedst La Hire in 1701, has 
been frequently used. Littrtuc's map-projection, an ortho- 
morphic projection In which the meridians are hyperbolas 
and the parallels ellipses, all these conies being confocal. 
This projection has two north and two south poles, all four 
coincident at infinity, and shows the sphere twice on two 
sheets, which are merely perversions of each other. It 
has many remarkable properties. It was Invented by the 
Bohemian astronomer Lit trow In 1 83S. Lorma't map-pro- 
jection. Same as iKwimc map-projection.- Map-projstnim 
by balance of error*, that zenithal projection which makes 
the " misrepresentation " a minimum, as determined by 
leaat squares. If r is the radius of an almucantar on the 
chart, z iu zenith distance, and Z that of the limit of the 
chart, which cannot exceed 126' 24' 53", then 
r = cot Jz log sec Jz + tan U cot-}Z log sec JZ. 
Map-projection by development, a projection upon a devel- 
opable surface which is then de\ -eloiHNl into a plane. Mer- 
cntnr'n map projection, an orthomorpbie map- projection in 
hieh tin- wllolesjihere isshown in equal repeating stripes. 
The point at infinity represents the whole sphere, and the 
zenith ami nadir do not elsewhere appear. As ordinarily 
used, the poles are taken as these points, when tile nieriil- 
ians appear as equidistant parallel lines, and the parallels 
as parallel lines cutting them at distances from the equator 
represents the whole earth on the sector of s circle, the 
pole being at the center and the parallels concentric cir- 
cles. It was Invented by J. H. Lambert Sttreoffraphic 
map-pro^etum, the simplest of all projection*, representing 
the whole sphere once on one Infinite plane, to 
tlnit) being considered as a point. All circlet t 
Meicator's Projection. 
tions all over the map. This projection, invented by the 
Flemish cosmographer Mercator in 1560, U the most use- 
ful of all. Meridvtnal map-projection, a map-projection 
which seems to be projected upon the plane ot a meridian, 
showing the poles at the extremities of a central meridian. 
Modyut Flamiteed's map-projection. Same a* Bonne'* 
map-projection.- MMiceidet map-projection. Same u Ao- 
motoyraphic map-projection Murdoch'* map- projection, 
one of three conical map-projections in which the part of the 
cone of which the map la a reduced development is equal 
to the spherical zone represented. These were Invented 
by fatrick Murdoch In 1788. Orthographic map-projection, 
a perspective map-projection from an Infinitely distant 
center. Orthmnorpnie map-projection, a map-projection 
which preserves all angles that U, the shape* of all in- 
finitesimal portions of the sphere. When one such map- 
projection has been obtained, say the polar stenographic, 
which Is the simplest, all others may be derived from this 
by a transformation of the plane. Let r and * be the polar 
coordinates of any point on the polar stereographlc pro- 
jection, let i denote the Imaginary whose square Is 1, 
and let F denote any function having a differential co- 
efficient If, then. K (rcos + rain .) be put Into the 
form x -(- yi, x and y will be the rectangular coordinates 
of the corresponding point on another orthomorphlc pro- 
jection. Also called conform map-projection. Paraucltt- 
aramniatic map-projection, a map projection in which the 
parallels are represented by equidistant straight lines, and 
the meridians by equidistant straight line* perpendicular 
to the parallels. This Is an ancient projection. Also called 
rfftaiiyulnr map-projection. Parent's map-projectvm, one 
of two perspective map-projection*. In Parent's tint 
map-projection the center ox projection is distant from 
the center of the sphere 1.586 times the radius. In his 
second this distance is 1.7Si Perspective map projection, 
a true projection of the sphere by straight lines from a 
center of projection intersecting the plane of the map. 
Petermann's map-projection, a discontinuous map-pro- 
jection showing tlie sphere in the form of an eight- 
pointed star. It Is used to decorate the title-page of 
stleler's atlas Polar map-projection, a map projection 
showing one of the poles in the center. Polycomc map- 
projection, a map-projection in which the surface of the 
earth Is cut Into an Infinite number of zone* parallel to 
the equator ; a central meridian Is then developed into a 
straight line, and then each zone 1* developed separately. 
This projection, Invented by Hasaler, superintendent of 
the United States Toast Survey, Is used In all government 
maps of the United State*. Quadrilateral map-projection, 
a broken equivalent projection in which one meridian has 
the form of a square, of which another meridian and the 
equator are the diagonals. It was invented by ColM- 
gnon. Quincuneial map projection, an orthomorphic pro- 
n*, repr 
, the part* at In- 
* on the sphere 
The World on a Qulncuncial Projection. 
jectlon of the earth Into repeating squares, Invented by C. 
s. i'elrce In lSi& Rectangular map-projection. Same as 
parallelogrammatic map-projection. uyeA' map-projec- 
tion, a conical projection in which the cone cut* the equator 
and has its vertex at one pole, and the sphere U projected 
upon the cone by lines perpendicular to the axis. It was In- 
vented by Kuyscb in 1508. Sanion's map-projection. Same 
.,-.,,,, i.l.il ;m;;.-;r', >.,</.. n. >'.-/n<ir/f I <;,<!/. /.r-i, -ctii'il a 
meridional map- projection in which the meridian* are rep- 
resented by ellipses cut at equal distances by the parallels. 
It was proposed by the physicist O. O. Schmidt in 1801. 
Sinumndal map-projection, an equivalent map projection 
in which the parallels are equidistant straight lines to 
which the central meridian is perpendicular. This pro- 
jection (so called from the form of the ni<ii<liana) was first 
used by the French chartographer Sanson In 1650. Spurn 
map-projection, the projection of a map which the succes- 
sive meridians and parallels cut up Into square*. Ste- 
Stereotcraphic Projection of the World 
are represented circles, and the angles are preserved. The 
stenographic projection of the sphere Is a perspective 
projection, a point on the surface lieing the center of pro- 
jection ; but the stereographlc map-projection of the sphe- 
roid Is not a perspective projection. The stereugraphlc 
projection was known to the ancients, and has always 
been employed for special purposes. Tertor's map-projec- 
tion, a modification of the tsocyllndrical map, DV J. ('. 
von '['eitor, 1808. Transverse map-projection, a meridional 
map- projection. Traperiform tnap prttjection, a map-pro, 
jection In which the space between two meridians and two 
parallels ia represented by a trapezoid, the sides of which 
are divided proportionally to determine other straight 
lines representing meridians and parallels. Werner'smap- 
projection, that equivalent map-projection which has the 
parallels concentric and equidistant arcs of circles, with 
the north pole at the center. The whole sphere has a heart 
shape. This was Invented by Johann Werner, 1514. Zen- 
ithalmap-projeclion,*n\*\t- projection which is symmetrical 
about a central point, the almucantars lieing represented 
by concentric circles. Mercator's projection. See 
Mert-ator's chart (under chart) and Mercator's map-projec- 
tion (above). Natural projection, a perspective delln- 
cation of a surface on a given plane. Stormmit A. Ob- 
lique projection, a cylindrical projection upon a plane 
not at right angles to the sides of the cylinder. Orthog- 
onal projection, a projection by means of rays all per- 
pendicular to the plane of projection. Orthographic 
projection. See under map-projection, above. Paral- 
lel projection, a perspective projection in whlcb the 
center U at infinity. - Plane of projection. Same as 
pempective plane (which see, under perspcctioe\ Pow- 
der Of projection. In alchemy, a powder added to 
base metals In a molten state, and supposed to have 
the power of transmuting them Into gold or silver. 
Stereoscopic projection, a double perspective projec- 
tion adapted to be viewed one part by one eye, the other 
by the other. 
projective (pro-jek'tiv), a. [< project + -ire.] 
1. Produced by projection. 2. In geom., re- 
lating to incidences and coincidences; not met- 
rical: as, a projective theorem or property. 3. 
Capable, as two plane figures, of Deing derived 
from one another by a 
number of projections 
and sections. Thus let 
the plane pencil OABCD be 
cut by the line AD In the 
point* A, B, C, D, and from 
the center P let these points 
be projected into the rays 
AE, BF, CO, DH, and let these 
be cut by the line KH in 
the point* K, F, O, H. Then, ABC 
the range of point* EFOH Projective I 
Is projective with the plane 
pencil OABCD. Projective geometry. See geometry. 
projectivity (pro-jek-tiv'j-ti), . [< projectors 
+ -ify.] The character of being projective, as 
two plane figures. 
projectmentt (pro-jekt'ment), *. [< project 
+ -me*t.] Projection; design; contrivance. 
[Rare.] 
She never doubted hut that men that were never so dis- 
honest in their projectments of each other's confusion 
might agree In their allegiance to her. 
Clarendon, Great Rebellion. 
projector (pro-jek'tor), M. [< NL. ' 
L. projicfre , proiccrr, \>\>. projecta*. proj-<-i 
/inyVrf."] 1. ( hit- who forms projects; one who 
forms a scheme or drMgn ; a schemer. 
