When division-lines, on measures of great nicety, get too fine to be read by the eye, we use the microscope.  By its means we are able to count 112,000 lines ruled on a glass plate within an inch.  The smallest object that can be seen by a keen eye makes an angle of 40”, but by putting six microscopes on the scale of the telescope on the mural circle, we are able to reach an exactness of 0".1, or 1/3600 of an inch.  This instrument is used to measure the declination of stars, or angular [Page 64] distance north or south of the equator.  Thus a star’s place in two directions is exactly fixed.  When the telescope is mounted on two pillars instead of the face of a wall, it is called a transit instrument.  This is used to determine the time of transit of a star over the meridian, and if the transit instrument is provided with a graduated circle it can also be used for the same purposes as the mural circle.  Man’s capacity to measure exactly is indicated in his ascertainment of the length of waves of light.  It is easy to measure the three hundred feet distance between the crests of storm-waves in the wide Atlantic; easy to measure the different wave-lengths of the different tones of musical sounds.  So men measure the lengths of the undulations of light.  The shortest is of the violet light, 154.84 ten-millionths of an inch.  By the horizontal pendulum Professor Root has made 1/36000000 of an inch apparent.

The next elements of accuracy must be perfect time and perfect notation of time.  As has been said, we get our time from the stars.  Thus the infinite and heavenly dominates the finite and earthly.  Clocks are set to the invariable sidereal time.  Sidereal noon is when we have turned ourselves under the point where the sun crosses the equator in March, called the vernal equinox.  Sidereal clocks are figured to indicate twenty-four hours in a day:  they tick exact seconds.  To map stars we wish to know the exact second when they cross the meridian, or the north and south line in the celestial dome above us.  The telescope (Fig. 21, p. 61) swings exactly north and south.  In its focus a set of fine threads of spider-lines is placed (Fig. 23).  The telescope is set just high enough, so that by the rolling over of the earth [Page 65] the star will come into the field just above the horizontal thread.  The observer notes the exact second and tenth of a second when the star reaches each vertical thread in the instrument, adds together the times and divides by five to get the average, and the exact time is reached.

[Illustration:  Fig. 23.—­Transit of a Star noted.]

But man is not reliable enough to observe and record with sufficient accuracy.  Some, in their excitement, anticipate its positive passage, and some cannot get their slow mental machinery in motion till after it has made the transit.  Moreover, men fall into a habit of estimating some numbers of tenths of a second oftener than others.  It will be found that a given observer will say three tenths or seven