168 CHRONOLOGICAL OBSERVATIONS. 



On further examining the properties of the indivisible elementary 

 numbers, it may be remarked, that 2 and 5 can in a measure be con- 

 cealed in 10 ; that 11 furnishes, as it were, two separate pivots for the 

 change of elements (as T * T + i£ = ? 4 ? + %% = 1) ; and that there remain 

 in fact but two working elements, 3 and 7; the sum of which, is also 10. 



I do not know, how far the above analysis of numbers may have 

 been previously noticed. The circumstance, that the Ancients rarely 

 made use of "fractions," has been pointed out to me: and from what 

 I witnessed among the people of Hindostan, I was led to suspect 

 the practice there of arithmetical processes which are unknown to 

 Europeans. 



15. An Astronomical fact remains to be mentioned. In Greece, the 

 atmosphere is so clear, that the stars are visible to the very edge of 

 the horizon. When sailing among the Greek islands, I was much 

 impressed with the spectacle presented by the constellation of the Great 

 Bear, the lowest of the bright stars not quite reaching the surface of 

 the ocean. It immediately occurred to me, that the same scene is 

 described by Homer (see II. xviii. 489, and Od. v. 275) : to the dis- 

 proving of an assertion, repeated in works of high standing; that even 

 at a later date than the clays of Homer, The star we call the pole-star 

 "was twelve degrees from the pole." 



That the axis of the Earth has pointed to about the same place in 

 the heavens ever since the days of Homer, is further proved from 

 Posidonius ; who gives a list of places along the shores of the Mediter- 

 ranean, where on proceeding south the star Canopus first becomes 

 visible (see his statement, as quoted by Cleomedes ii. 10, and by 

 Strabo ii.). I do not know, whether any verification of these obser- 

 vations has been made in Modern times ; but I am persuaded that if 

 a change has taken place, it will prove to be extremely slight. 



