tenths oftener than four or eight.  He is falling into ruts, and not trustworthy.  General O. M. Mitchel, who had been director of the Cincinnati Observatory, once told one of his staff-officers that he was late at an appointment.  “Only a few minutes,” said the officer, apologetically.  “Sir,” said the general, “where I have been accustomed to work, hundredths of a second are too important to be neglected.”  And it is to the rare genius of this astronomer, and to others, that we owe the mechanical accuracy that we now attain.  The 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.