c telegraphs.

In Watt's indicator for steam engines the paper does not move with a
constant velocity, but its displacement is proportional to that of the
piston of the engine, while that of the tracing point is proportional
to the pressure of the steam. Hence the co-ordinates of a point of the
curve traced on the diagram represent the volume and the pressure of
the steam in the cylinder. The indicator-diagram not only supplies a
record of the pressure of the steam at each stage of the stroke of the
engine, but indicates the work done by the steam in each stroke by the
area enclosed by the curve traced on the diagram. (J. C. M.)

DIAL and DIALLING. Dialling, sometimes called gnomonics, is a branch of
applied mathematics which treats of the construction of sun-dials, that
is, of those instruments, either fixed or portable, which determine the
divisions of the day (Lat. _dies_) by the motion of the shadow of some
object on which the sun's rays fall. It must have been one of the
earliest applications of a knowledge of the apparent motion of the sun;
though for a long time men would probably be satisfied with the division
into morning and afternoon as marked by sun-rise, sun-set and the
greatest elevation.

_History._--The earliest mention of a sun-dial is found in Isaiah
xxxviii. 8: "Behold, I will bring again the shadow of the degrees which
is gone down in the _sun-dial_ of Ahaz ten degrees backward." The date
of this would be about 700 years before the Christian era, but we know
nothing of the character or construction of the instrument. The earliest
of all sun-dials of which we have any certain knowledge was the
hemicycle, or hemisphere, of the Chaldaean astronomer Berossus, who
probably lived about 300 B.C. It consisted of a hollow hemisphere placed
with its rim perfectly horizontal, and having a bead, or globule, fixed
in any way at the centre. So long as the sun remained above the horizon
the shadow of the bead would fall on the inside of the hemisphere, and
the path of the shadow during the day would be approximately a circular
arc. This arc, divided into twelve equal parts, determined twelve equal
intervals of time for that day. Now, supposing this were done at the
time of the solstices and equinoxes, and on as many intermediate days as
might be considered sufficient, and then curve lines drawn through the
corresponding points of division of the different arcs, the shadow of
the bead