f these. A universal dial was
constructed of a figure in the shape of a cross; another universal
dial showed the hours by a globe and by several gnomons. These
universal dials required adjusting before use, and for this a
mariner's compass and a spirit-level were necessary. But it would be
tedious and useless to enumerate the various forms designed, and, as a
rule, the more complex the less accurate.

Another class of useless dials consisted of those with variable
centres. They were drawn on fixed horizontal planes, and each day the
style had to be shifted to a new position. Instead of hour-_lines_
they had hour-_points_; and the style, instead of being parallel to
the axis of the earth, might make any chosen angle with the horizon.
There was no practical advantage in their use, but rather the reverse;
and they can only be considered as furnishing material for new
mathematical problems.

_Portable Dials._--The dials so far described have been fixed dials,
for even the fanciful ones to which reference was just now made were
to be fixed before using. There were, however, other dials, made
generally of a small size, so as to be carried in the pocket; and
these, so long as the sun shone, roughly answered the purpose of a
watch.

The description of the portable dial has generally been mixed up with
that of the fixed dial, as if it had been merely a special case, and
the same principle had been the basis of both; whereas there are
essential points of difference between them, besides those which are
at once apparent.

In the fixed dial the result depends on the _uniform_ angular motion
of the sun round the fixed style; and a small error in the assumed
position of the sun, whether due to the imperfection of the
instrument, or to some small neglected correction, has only a trifling
effect on the time. This is owing to the angular displacement of the
sun being so rapid--a quarter of a degree every minute--that for the
ordinary affairs of life greater accuracy is not required, as a
displacement of a quarter of a degree, or at any rate of one degree,
can be readily seen by nearly every person. But with a portable dial
this is no longer the case. The uniform angular motion is not now
available, because we have no determined fixed plane to which we may
refer it. In the new position, to which the observer has gone, the
zenith is the only point of the heav