SEQUEL TO THE EPOCH OF HIPPAECHUS. 159 



thought himself justified in asserting that the years were always ex 

 actly equal, he showed, both by observations of the time when the sun 

 passed the equinoxes, and by eclipses, that the difference of successive 

 years, if there were any difference, must be extremely slight. The 

 observations of succeeding astronomers, and especially of Ptolemy, 

 confirmed this opinion, and proved, with certainty, that there is no 

 progressive increase or diminution in the duration of the year. 



3. Constant Length of Days. Equation of Time. — The equality of 

 days was more difficult to ascertain than that of years ; for the year 

 is measured, as on a natural scale, by the number of days which it 

 contains ; but the day can be subdivided into hours only by artificial 

 means ; and the mechanical skill of the ancients did not enable them 

 to attain any considerable accuracy in the measure of such portions of 

 time ; though clepsydras and similar instruments were used by astron- 

 omers. The equality of days could only be proved, therefore, by the 

 consequences of such a supposition ; and in this manner it appears to 

 have been assumed, as the fact really is, that the apparent revolution 

 of the stars is accurately uniform, never becoming either quicker or 

 slower. It followed, as a consequence of this, that the solar days (or 

 rather the mjcthemers, compounded of a night and a day) would be 

 unequal, in consequence of the sun's unequal motion, thus giving rise 

 to what we now call the Equation of Time, — the interval by which 

 the time, as marked on a dial, is before or after the time, as indicated 

 by the accurate timepieces which modern skill can produce. This 

 inequality was fully taken account of by the ancient astronomers ; and 

 they thus in fact assumed the equality of the sidereal days. 



Sect. 2. — Researches which did not verify the Theory. 



Some of the researches of Hipparchus and his followers fell upon 

 the weak parts of his theory ; and if the observations had been suffi- 

 ciently exact, must have led to its being corrected or rejected. 



Among these we may notice the researches which were made con- 

 cerning the Parallax of the heavenly bodies, that is, their apparent 

 displacement by the alteration of position of the observer from one 

 part of the earth's surface to the other. This subject is treated of at 

 length by Ptolemy; and there can be no doubt that it was well ex- 

 amined by Hipparchus, who invented a parallactic instrument for that 

 purpose. The idea of parallax, as a geometrical possibility, was indeed 

 too obvious to be overlooked by geometers at any time ; and when the 

 doctrine of the sphere was established, it must have appeared strange 



