ough the
influence of Sir Isaac Newton he was elected mathematical master in
Christ's hospital. He was author of the following memoirs and
treatises:--"Of the Tangents of Curves, &c.," _Phil. Trans._ vol.
xxiii.; "A Treatise on Spherical Catoptrics," published in the _Phil.
Trans._ vol. xxiv., from which it was copied and reprinted in the _Acta
Eruditorum_ (1707), and also in the Memoirs of the Academy of Sciences
at Paris; _General Laws of Nature and Motion_ (1705), a work which is
commended by Wolfius as illustrating and rendering easy the writings of
Galileo and Huygens, and the _Principia_ of Newton; _An Institution of
Fluxions, containing the First Principles, Operations, and Applications
of that admirable Method, as invented by Sir Isaac Newton_ (1706). In
1709 he published the _Synopsis Algebraica_ of John Alexander, with many
additions and corrections. In his _Treatise on Perspective_ (1712) he
explained the mathematical principles of that art; and anticipated the
method afterwards elaborated by Brook Taylor. In 1714 Ditton published
his _Discourse on the Resurrection of Jesus Christ;_ and _The New Law of
Fluids, or a Discourse concerning the Ascent of Liquids in exact
Geometrical Figures, between two nearly contiguous Surfaces_. To this
was annexed a tract ("Matter not a Cogitative Substance") to demonstrate
the impossibility of thinking or perception being the result of any
combination of the parts of matter and motion. There was also added an
advertisement from him and William Whiston concerning a method for
discovering the longitude, which it seems they had published about half
a year before. Although the method had been approved by Sir Isaac Newton
before being presented to the Board of Longitude, and successfully
practised in finding the longitude between Paris and Vienna, the board
determined against it. This disappointment, aggravated as it was by
certain lines written by Dean Swift, affected Ditton's health to such a
degree that he died in the following year, on the 15th of October 1715.

DIU, an island and town of India, belonging to Portugal, and situated at
the southern extremity of the peninsula of Kathiawar. Area of district,
20 sq. m. Pop. (1900) 14,614. The anchorage is fairly protected from the
sea, but the depth of water is only 3 to 4 fathoms. The channel between
the island on Diu and the mainland is navigable only by fishing boats
and small craft. The town is well fortified on the old sy