clock is made to mark its seconds on paper wrapped
around a revolving cylinder. Under the observer's fingers is an
electric key. This he can touch at the instant of the transit of
the star [Page 66] over each wire, and thus put his observation on
the same line between the seconds dotted by the clock. Of course
these distances can be measured to minute fractional parts of a
second.

But it has been found that it takes an appreciable time for every
observer to get a thing into his head and out of his finger-ends,
and it takes some observers longer than others. A dozen men, seeing
an electric spark, are liable to bring down their recording marks
in a dozen different places on the revolving paper. Hence the time
that it takes for each man to get a thing into his head and out
of his fingers is ascertained. This time is called his personal
equation, and is subtracted from all of his observations in order to
get at the true time; so willing are men to be exact about material
matters. Can it be thought that moral and spiritual matters have
no precision? Thus distances east or west from any given star or
meridian are secured; those north and south from the equator or
the zenith are as easily fixed, and thus we make such accurate
maps of the heavens that any movements in the far-off stars--so
far that it may take centuries to render the swiftest movements
appreciable--may at length be recognized and accounted for.

[Illustration: Fig. 24.]

We now come to a little study of the modes of measuring distances.
Create a perfect square (Fig. 24); draw a diagonal line. The square
angles are 90 deg., the divided angles give two of 45 deg. each. Now the
base A B is equal to the perpendicular A C. Now any point--C, where
a perpendicular, A C, and a diagonal, B C, meet--will be [Page 67]
as far from A as B is. It makes no difference if a river flows
between A and C, and we cannot go over it; we can measure its
distance as easily as if we could. Set a table four feet by eight
out-doors (Fig. 25); so arrange it that, looking along one end, the
line of sight just strikes a tree the other side of the river. Go to
the other end, and, looking toward the tree, you find the line of
sight to the tree falls an inch from the end of the table on the
farther side. The lines, therefore, approach each other one inch in
every four feet, and will come together at a tree three hundred and
eighty-four feet away.

[Illustration: Fig. 25.--Measuring Dista