THE BEGINNINGS OF CERTITUDE 53 



as they are held in prayer. Little by little, in what manner is 

 hidden from our view, grew up the complicated systems which ap- 

 pear in the earliest of the clay tablets which have been unearthed. 



It must have all been very old. Some of the Sumerian 

 inscriptions, forerunners of the Babylonian, reveal the existence 

 of a sexagesimal system that is to say, in which the count 

 extended up to sixty and there begins over again. It was long, 

 probably, before the count extended up to a hundred and began 

 again there. But why was this especial number of sixty chosen ? 

 We can only conclude that by this time something of the pro- 

 perties of circles and radii had already become known. This 

 in turn had obviously come from their endeavour to forefigure 

 the year, the path of the moon, and all the like. 



Doubtless the earliest of external phenomena which ancient 

 man came to study with attention was the changing length of 

 nights and days, the succession of heat and cold, the return of 

 the seasons. When he had begun to seek a more stable food- 

 supply than from the precarious providence of nature, he needed 

 a sign for the time to plant his crops. When he had organised 

 into tribes and perhaps begun to barter his labour for produce, 

 there came the need of a means of reckoning time. The going 

 and coming of the moon gave him a unit for a bundle of days. 

 He needed a larger, which should fix the return of spring. 



As he watched the heavens he saw that the position of the 

 stars at nightfall and at dawn, with reference to the sun, appears 

 to change. It was a generalisation of a high order when he 

 had reached the conception that the stars are stable, and that 

 it is the sun, the bringer of the day, which in reality changes 

 its place. Attentively observing the changing rising point and 

 setting point of the sun, the primitive astronomers saw that 

 it swept through a seeming circle in the air. From this 

 perhaps came the Latin word for the year, annus, whence our 

 word " annual," meaning a " ring " ; it appears primitively to 

 have signified simply a " bending." The sun in his shift of 

 position seemed to describe a continuous bending, which in 

 the end brought it back to the same point. 



The reckoning doubtless was not very close ; there was a 

 convenience in round numbers. In the beginning they appear 

 to have fixed the number of days within this period at three 

 hundred and sixty. Doubtless from this the study of the 

 circle began. When they had found that a regular figure of 



