PROGRESS IN ANTIQUITY. 25 



Apsides ; 5, formed the earliest Tables of the Sun, and 

 calculated with accuracy when lunar and solar eclipses would 

 occur; 6, determined the period of the moon's revolution, 

 relatively to the stars, to the sun, to her own nodes, and to her 

 apogee determinations which furnish one of the most delicate 

 tests of the truth of Newton's law of gravitation ; 7, determined 

 the eccentricity of the lunar orbit and its inclination to the 

 plane of the ecliptic ; formed Lunar Tables (and is therefore 

 the discoverer of the mode of constructing solar and lunar 

 tables) ; 8, approximated to the parallax of the moon ; 9, 

 catalogued 1,080 stars, and showed how they are situated 

 and grouped with relation to the ecliptic ; 10, invented the 

 planisphere or mode of representing the starry heavens upon 

 a plane, and of producing the solutions of problems of 

 spherical astronomy ; 11, devised the application of parallax 

 to determine the distances of celestial bodies ; 12, demon- 

 strated the methods of calculating triangles, whether recti- 

 lineal or spherical which may be considered as the beginning 

 of Trigonometry; 13, had the happy idea, for assisting 

 Geography, of fixing the positions of spots on the earth by 

 means of the latitudes and longitudes completing thereby 

 Eratosthenes's Geography ; 14, was the first who determined 

 the longitude by the eclipses of the moon; 15, constructed 

 a TABLE OF CHORDS, of which he made the same use as we 

 make of our sines ; 16, made use of the dioptra, and 

 invented the parallelic instrument and the ASTROLABE ; 17, 

 discovered the PRECESSION OF THE EQUINOXES a gradual 

 change in the position of the nodes (intersecting points) of 

 the earth's equator on the ecliptic. The nature of this 

 change is such that the nodes of the celestial equator on the 

 ecliptic in other words, " the first points of Aries and Libra 

 are continually travelling along the ecliptic in a direction 

 contrary to the order of the signs/' The intersection this 

 year, for instance, occurs at a point just before last year's 

 point (hence the name of precession), and occurs more to the 

 west every year by 5o"'2i ; so that the nodes shift retro- 

 gressively one degree in 71*6 years a complete revolution 

 of the nodes being accomplished in 25,866 years. This is one 

 of the most important discoveries in the world of science, and 



