), Euler
and Lambert helped in developing the theory, and much was done by
Lagrange in his additions to the French edition of Euler's _Algebra_
(1795). Moritz A. Stern wrote at length on the subject in _Crelle's
Journal_ (x., 1833; xi., 1834; xviii., 1838). The theory of the
convergence of continued fractions is due to Oscar Schloemilch, P. F.
Arndt, P. L. Seidel and Stern. O. Stolz, A. Pringsheim and E. B. van
Vleck have written on the convergence of infinite continued fractions
with complex elements.

REFERENCES.--For the further history of continued fractions we may
refer the reader to two papers by Gunther and A. N. Favaro,
_Bulletins di bibliographia e di storia delle scienze mathematische e
fisicke_, t. vii., and to M. Cantor, _Geschichte der Mathematik_, 2nd
Bd. For text-books treating the subject in great detail there are
those of G. Chrystal in English; Serret's _Cours d`algebre
superieure_ in French; and in German those of Stern, Schloemilch,
Hatterdorff and Stolz. For the application of continued fractions to
the theory of irrational numbers there is P. Bachmann's _Vorlesungen
ueber die Natur der Irrationalzahnen_ (1892). For the application of
continued fractions to the theory of lenses, see R. S. Heath's
_Geometrical Optics_, chaps. iv. and v. For an exhaustive summary of
all that has been written on the subject the reader may consult Bd. 1
of the _Encyklopaedie der mathematischen Wissenschaften_ (Leipzig).
(A. E. J.)

CONTOUR, CONTOUR-LINE (a French word meaning generally "outline," from
the Med. Lat. _contornare_, to round off), in physical geography a line
drawn upon a map through all the points upon the surface represented
that are of equal height above sea-level. These points lie, therefore,
upon a horizontal plane at a given elevation passing through the land
shown on the map, and the contour-line is the intersection of that
horizontal plane with the surface of the ground. The contour-line of 0,
or _datum level_, is the coastal boundary of any land form. If the sea
be imagined as rising 100 ft., a new coast-line, with bays and estuaries
indented in the valleys, would appear at the new sea-level. If the sea
sank once more to its former level, the 100-ft. contour-line with all
its irregularities would be represented by the beach mark made by the
sea when 100 ft. higher. If instead of receding the sea rose
continuously at the rate of 100 ft. per day