es marked
as follows:-January 10, 20, 31; February 10, 20, 28; March 10, 20, 31;
April 10, 20, 30, and so on,--always the 10th, the 20th, and the last
day of each month.

[Illustration: FIG. 7.]

Through each point of division a vertical line parallel to the axis of
the cylinder is drawn from top to bottom. Now it will be readily
understood that if, upon one of these days, the lid be turned, so as
to bring the style exactly opposite the date, and if the dial be then
placed on a horizontal table so as to receive sunlight, and turned
round bodily until the shadow of the style falls exactly on the
vertical line below it, the shadow will terminate at some definite
point of this line, the position of which point will depend on the
length of the style--that is, the distance of its end from the surface
of the cylinder--and on the altitude of the sun at that instant.
Suppose that the observations are continued all day, the cylinder
being very gradually turned so that the style may always face the sun,
and suppose that marks are made on the vertical line to show the
extremity of the shadow at each exact hour from sun-rise to
sun-set-these times being taken from a good fixed sun-dial,--then it is
obvious that the next year, on the _same date_, the sun's declination
being about the same, and the observer in about the same latitude, the
marks made the previous year will serve to tell the time all that day.

What we have said above was merely to make the principle of the
instrument clear, for it is evident that this mode of marking, which
would require a whole year's sunshine and hourly observation, cannot
be the method employed.

The positions of the marks are, in fact, obtained by calculation.
Corresponding to a given date, the declination of the sun is taken
from the almanac, and this, together with the latitude of the place
and the length of the style, will constitute the necessary data for
computing the length of the shadow, that is, the distance of the mark
below the style for each successive hour.

We have assumed above that the declination of the sun is the same at
the same date in different years. This is not quite correct, but, if
the dates be taken for the second year after leap year, the results
will be sufficiently approximate.

When all the hour-marks have been placed opposite to their respective
dates, then a continuous curve, joining t