ORIGIN OF GEOMETRICAL ASTRONOMY. 171 



increasiug number of previsions, bat towards previsions 

 more accurately quantitative — how, in astronomy, the re- 

 curring period of the moon's motions was by and by more 

 correctly ascertained to be nineteen years, or two hundred 

 and thirty-five lunations ; how Callipus further corrected 

 this Metonic cycle, by leaving out a day at the end of every 

 seventy-six years ; and how these successive advances im 

 pliecl a longer continued registry of observations, and the 

 co-ordination of a greater number of facts — let us go on to 

 inquire how geometrical astronomy took its rise. 



The first astronomical instrument was the gnomon 

 This was not only early in use in the East, but it was found 

 also among the Mexicans ; the sole astronomical observa- 

 tions of the Peruvians were made by it ; and we read that 

 1100 B.C., the Chinese found that, at a certain place, the 

 length of the sun's shadow, at the summer solstice, was to 

 the height of the gnomon, as one and a half to eight. 

 Here again it is observable, not only that the instrument is 

 found ready made, but that Nature is perpetually perform- 

 ing the process of measurement. Any fixed, erect object 

 — a column, a dead palm, a pole, the angle of a building — 

 serves for a gnomon ; and it needs but to notice the chang- 

 ing position of the shadow it daily throws, to make the 

 first step in geometrical astronomy. How small this first 

 step was, may be seen in the fact that the only things as- 

 certained at the outset were the periods of the summer 

 and winter solstices, which corresponded with the least and 

 greatest lengths of the mid-day shadow ; and to fix which, 

 it was needful merely to mark the point to w^hich each 

 day's shadow reached. 



And now let it not be overlooked that in the observing 

 at what time during the next year this extreme limit of the 

 i^hadow was again reached, and in the inference that the 

 sun had then arrived at the same turning point in his an- 

 Qual course, we have one of the simplest instances of tliat 



