[Illustration:  Fig. 28.]

It is obvious that if one star were three times as far from us as another, the nearer one would seem to be displaced by our movement in our orbit three times as much as the other; so, by comparing one star with another, we reach a ground of judgment.  The ascertainment of longitude at sea by means of the moon affords a good illustration.  Along the track where the moon sails, nine bright stars, four planets, and the sun have been selected.  The nautical almanacs give the distance of the moon from these successive stars every hour in the night for three years in advance.  The sailor can measure the distance at any time by his sextant.  Looking from the world at D (Fig. 29), the distance of the moon and [Page 72] star is A E, which is given in the almanac.  Looking from C, the distance is only B E, which enables even the uneducated sailor to find the distance, C D, on the earth, or his distance from Greenwich.

[Illustration:  Fig. 29.—­Mode of Ascertaining Longitude.]

So, by comparisons of the near and far stars, the approximate distance of a few of them has been determined.  The nearest one is the brightest star in the Centaur, never visible in our northern latitudes, which has a parallax of about one second.  The next nearest is No. 61 in the Swan, or 61 Cygni, having a parallax of 0".34.  Approximate measurements have been made on Sirius, Capella, the Pole Star, etc., about eighteen in all.  The distances are immense:  only the swiftest agents can traverse them.  If our earth were suddenly to dissolve its allegiance to the king of day, and attempt a flight to the North Star, and should maintain its flight of one thousand miles a minute, it would flyaway toward Polaris for thousands upon thousands of years, till a million years had passed away, before it reached that northern dome of the distant sky, and gave its new allegiance to another sun.  The sun it had left behind it would gradually diminish till it was small as Arcturus, then small as could be discerned by the naked eye, until at last it would finally fade out in utter darkness long before the new sun was reached.  Light can traverse the distance around our earth eight times in one second.  It comes in eight minutes from the sun, but it takes three and a quarter years to come from Alpha [Page 73] Centauri, seven and a quarter years from 61 Cygni, and forty-five years from the Polar Star.

Sometimes it happens that men steer along a lee shore, dependent for direction on Polaris, that light-house in the sky.  Sometimes it has happened that men have traversed great swamps by night when that star was the light-housse of freedom.  In either case the exigency of life and liberty was provided for forty-five years before by a Providence that is divine.

We do not attempt to name in miles these enormous distances; we must seek another yard-stick.  Our astronomical unit and standard of measurement is the distance of the earth from the sun—­92,500,000 miles.  This is the golden reed with which we measure the celestial city.  Thus, by laying down our astronomical unit 226,000 times, we measure to Alpha Centauri, more than twenty millions of millions of miles.  Doubtless other suns are as far from Alpha Centauri and each other as that is from ours.