Archaic Sculptitrings. 135 



the swollen part. Many instances in Scotland and elsewhere 

 of the number nine occurring in connection with circular 

 movements in ancient customs will readily be recollected by 

 the student of folk-lore. 



There mav be noted in these sculpturings many more or 

 less uniform numerical relationships and the adherence to a 

 unit of measurement, which was carried over from pre- 

 historic to proto-historic and to modern times. It seems also 

 clear that the essential component parts of a group are placed 

 at definitely pre-arranged distances from the focal point, fol- 

 lowing some system. 



On examining the astronomical ideas prevailing in Baby- 

 lonia and in ancient Egypt, Persia, and India, and also the 

 ideas worked up in the sixth century before Christ, and in 

 the few subsequent centuries by the Pythagoreans, a series 

 of analogies with the pre-historic cup-and-ring markings and 

 with the ground plans of certain pre-historic structures seems 

 to emerge. Taking the Pythagorean astronomy as derived in 

 its basic concept from still more ancient cults, and as one 

 regarding which a good deal is known, it is well understood 

 that the main idea was the central place from which fire, 

 light, life, and all power emanated. This " Hearth of the 

 Universe " was called " Hestia " or the " Watch-Tower ot 

 Zeus," and various peoples have called it by many names. 

 Round about it were supposed to revolve ten bodies, their 

 distances from the central point being dictated by simple 

 numerical relations deri\ed from the lengths of strings, 

 which, if struck simultaneously, produced a harmony of 

 sound. 



The revolving body next to the " Central Fire " was 

 called " Counter-Earth." The next again was Earth, then 

 beyond that the Moon, then the Sun. Farther out were the 

 bodies of the five planets then known. Beyond them was the 

 outmost revolving body the " Heaven and fixed stars." The 

 " Central Fire " and the " Counter-Earth " were supposed to 

 be invisible. The latter was imaginary, though its existence 

 was believed in. Its presence was inferred as it accounted 

 for eclipses and darkness. The change in the positions of 

 the earth and sun were supposed to produce night and day, 



