/ 1. Cylindrical equal-area.
| 2. Orthographic.
| 3. Stereographic (which is orthomorphic).
Perspective < 4. General external perspective.
| 5. Minimum error " (Clarke's).
\ 6. Central.
/ 7. Conical, with rectified meridians and two
| standard parallels (5 forms).
| 8. Simple conical.
| 9. Simple cylindrical (a special case of 8).
| 10. Modified conical equal-area (Bonne's).
| 11. Sinusoidal " " (Sanson's).
| 12. Werner's conical " "
Conical < 13. Simple polyconic.
| 14. Rectangular polyconic.
| 15. Conical orthomorphic with 2 standard parallels
| (Lambert's, commonly called Gauss's).
| 16. Cylindrical orthomorphic (Mercator's).
| 17. Conical equal-area with one standard parallel.
| 18. " " " " two " parallels.
\ 19. Projection by rectangular spheroidal co-ordinates.
/ 20. Equidistant zenithal.
| 21. Zenithal equal-area.
| 22. Zenithal projection by balance of errors (Airy's).
Zenithal < 23. Elliptical equal-area (Mollweide's).
| 24. Globular (conventional).
\ 25. Field sheet graticule.
Of the above 25 projections, 23 are conical or quasi-conical, if
zenithal and perspective projections be included. The projections may,
if it is preferred, be grouped according to their properties. Thus in
the above list 8 are equal-area, 3 are orthomorphic, 1 balances
errors, 1 represents all great circles by straight lines, and in 5 one
system of great circles is represented correctly.
Among projections which have not been described may be mentioned the
circular orthomorphic (Lagrange's) and the rectilinear equal-area
(Collignon's) and a considerable number of conventional projections,
which latter are for the most part of little value.
The choice of a projection depends on the function which the map is
intended to fulfil. If the map is intended for statistical purposes to
show areas, density of population, incidence of rainfall, of disease,
distribution of wealth, &c., an _equal-area_ projection should be
chosen. In such a case an area scale should be given. At sea,
_Mercator's_ is practically the only projection used except when it is
desired to determine graphically great circle courses in great oceans,
when the _central_ projection must be employed. For conveying good
general ideas of the shape and distribution of the surface features of
continents or of a hemisphere _Clarke's perspective_ projection is the
best. For exhibiting the progress of polar exploration the _polar
equidistant_ projection should be selected. For special maps for
general use on scales of 1/1,000,000 and smaller, and for a series of
which the sheets are to fit together, the _conical, with rectified
meridians and two standard parallels_, is a good projection. For
topographical maps, in which each sheet is plotted independently and
the scale is not smaller than 1/500,000, either form of _polyconic_ is
very convenient.
The following are the projections adopted for some of the principal
official maps of the British Empire:--
_Conical, with Rectified Meridians and Two Standard Parallels._--The
1:1,000,000 Ordnance map of the United Kingdom, special maps of the
topographical section, General Staff, e.g. the 64-mile map of
Afghanistan and Persia. The 1:1,000,000 Survey of India series of
India and adjacent countries.
_Modified Conical, Equal-area (Bonne's)._--The 1 in., ½ in., ¼ in. and
1/10 in. Ordnance maps of Scotland and Ireland. The 1:800,000 map of
the Cape Colony, published by the Surveyor-General.
_Simple Polyconic and Rectangular Polyconic_ maps on scales of
1:1,000,000, 1:500,000, 1:250,000 and 1:125,000 of the topographical
section of the General Staff, including all maps on these scales of
British Africa. A rectilinear approximation to the simple polyconic is
also used for the topographical sheets of the Survey of India. The
simple polyconic is used for the 1 in. maps of the Militia Department
of Canada.
_Zenithal Projection by Balance of Errors (Airy's)._--The 10-mile to 1
in. Ordnance map of England.
_Projection by Rectangular Spheroidal Co-ordinates._--The 1:2500 and
the 6 in. Ordnance sheets of the United Kingdom, and the 1 in., ½ in.
and ¼ in. Ordnance maps of England. The cadastral plans of the Survey
of India, and cadastral plans throughout the empire.
AUTHORITIES.--See _Traité des projections des cartes géographiques_,
by A. Germain (Paris, 1865) and _A Treatise on Projections_, by T.
Craig, United States Coast and Geodetic Survey (Washington, 1882).
Both Germain and Craig (following Germain) make use of the term
_projections by development_, a term which is apt to convey the
impression that the spherical surface is developable. As this is not
the case, and since such projections are conical, it is best to avoid
the use of the term. For the history of the subject see d'Avezac,
"Coup d'oeil historique sur la projection des cartes géographiques,"
_Société de géographie de Paris_ (1863).
J. H. Lambert (_Beiträge zum Gebrauch der Mathematik, u.s.w._ Berlin,
1772) devised the following projections of the above list: 1, 15, 17,
and 21; his transverse cylindrical orthomorphic and the transverse
cylindrical equal-area have not been described, as they are seldom
used. Among other contributors we mention Mercator, Euler, Gauss, C.
B. Mollweide (1774-1825), Lagrange, Cassini, R. Bonne (1727-1795),
Airy and Colonel A. R. Clarke. (C. F. Cl.; A. R. C.)