([delta]) _Function Theories of Non-Linear Ordinary
Equations_:--Painleve, _Lecons sur la theorie analytique des equations
differentielles_ (Paris, 1897, Autographed); Forsyth, _Theory of
Differential Equations, Part ii., Ordinary Equations not Linear_ (two
volumes, ii. and iii.) (Cambridge, 1900); Konigsberger, _Lehrbuch der
Theorie der Differentialgleichungen_ (Leipzig, 1889); Painleve,
_Lecons sur l'integration des equations differentielles de la
mecanique et applications_ (Paris, 1895).

([epsilon]) _Formal Theories of Partial Equations of the Second and
Higher Orders_:--E. Goursat, _Lecons sur l'integration des equations
aux derivees partielles du second ordre_, tt. i. and ii. (Paris, 1896,
1898); Forsyth, _Treatise on Differential Equations_ (London, 1889);
and _Phil. Trans. Roy. Soc._ (A.), vol. cxci. (1898), pp. 1-86.

([zeta]) See also the six extensive articles in the second volume of
the German _Encyclopaedia of Mathematics_. (H. F. BA.)

DIFFLUGIA (L. Leclerc), a genus of lobose Rhizopoda, characterized by a
shell formed of sand granules cemented together; these are swallowed by
the animal, and during the process of bud-fission they pass to the
surface of the daughter-bud and are cemented there. _Centropyxis_
(Steia) and _Lecqueureuxia_ (Schlumberg) differ only in minor points.

DIFFRACTION OF LIGHT.--1. When light proceeding from a small source
falls upon an opaque object, a shadow is cast upon a screen situated
behind the obstacle, and this shadow is found to be bordered by
alternations of brightness and darkness, known as "diffraction bands."
The phenomena thus presented were described by Grimaldi and by Newton.
Subsequently T. Young showed that in their formation interference plays
an important part, but the complete explanation was reserved for A. J.
Fresnel. Later investigations by Fraunhofer, Airy and others have
greatly widened the field, and under the head of "diffraction" are now
usually treated all the effects dependent upon the limitation of a beam
of light, as well as those which arise from irregularities of any kind
at surfaces through which it is transmitted, or at which it is
reflected.

2. _Shadows._--In the infancy of the undulatory theory the objection
most frequently urged against it was the difficulty of explaining the
very existence of shadows. Thanks to Fresnel and his followers, this
department of optics is now precisely the one in