[Illustration:  Fig. 20.—­Illustration of Angles.]

Imagine yourself inside a perfect sphere one hundred feet in diameter, with the interior surface above, around, and below studded with fixed bright points like stars.  The familiar constellations of night might be blazoned there in due proportion.

If this star-sprent sphere were made to revolve once in twenty-four hours, all the stars would successively [Page 60] pass in review.  How easily we could measure distances between stars, from a certain fixed meridian, or the equator!  How easily we could tell when any particular star would culminate!  It is as easy to take all these measurements when our earthly observatory is steadily revolved within the sphere of circumambient stars.  Stars can be mapped as readily as the streets of a great city.  Looking down on it in the night, one could trace the lines of lighted streets, and judge something of its extent and regularity.  But the few lamps of evening would suggest little of the greatness of the public buildings, the magnificent enterprise and commerce of its citizens, or the intelligence of its scholars.  Looking up to the lamps of the celestial city, one can judge something of its extent and regularity; but they suggest little of the magnificence of the many mansions.

Stars are reckoned as so many degrees, minutes, and seconds from each other, from the zenith, or from a given meridian, or from the equator.  Thus the stars called the Pointers, in the Great Bear, are 5 deg. apart; the nearest one is 29 deg. from the Pole Star, which is 39 deg. 56’ 29” above the horizon at Philadelphia.  In going to England you creep up toward the north end of the earth, till the Pole Star is 54 deg. high.  It stays near its place among the stars continually,

 “Of whose true-fixed and resting quality
  There is no fellow in the firmament.”

How to Measure.

Suppose a telescope, fixed to a mural circle, to revolve on an axis, as in Fig. 21; point it horizontally at a star; [Page 61] turn it up perpendicular to another star.  Of course the two stars are 90 deg. apart, and the graduated scale, which is attached to the outer edge of the circle, shows a revolution of a quarter circle, or 90 deg., But a perfect accuracy of measurement must be sought; for to mistake the breadth of a hair, seen at the distance of one hundred and twenty-five feet, would cause an error of 3,000,000 miles at the distance of the sun, and immensely more at the distance of the stars.  The correction of an inaccuracy of no greater magnitude than that has reduced our estimate of the distance of our sun 3,000,000 miles.

[Illustration:  Fig. 21.—­Mural Circle.]