200 



KNOWLEDGE. 



[Sbptbmbeb, 1902. 



was multiplied 1)y lO, then the prodiu^t was iniiiti])lied 

 by 1(1, and then the ivsult was inultipliod l)y lO. 'i'lic 

 oriffinal nuinlior was thus triply intonsilicd, iind by this 

 moans totals were attained, not literally trui', Imt, merely 

 expressions of vastness in the number of thini^s or of 

 years. It is necessary to say this much in illustration of 

 the facts of the case. The central (zodiacal) circle was 

 already, in the nature of things, connected with the 

 number 12 ; and this mode of intensive expansion raised it 

 to 120 divisions or degrees. I do not, however, assert 

 that this principle is the only link between 10 and 12 in 

 the matter. These circles thus showing a sexagesimal 

 method, we find, as might be expected, the same ]>rin(ii)le 

 cimfirmed by the c\ineiform writing. The sinL,'ie weclge 

 which represents ' 1 ' also stands for 't>0.' In Eupliratean 

 computation 60 is also the unexpressed denominator of a 

 fraction ; and we possess a tablet which ' gives a table of 

 si|uari's and cubes correctly calculated from 1 to 00.' The 

 iiiluiliitants of the Euphrates Valley further ' sub-divided 

 the unit into 00 equal parts, and each of these parts into 

 (50 further equal sub-divisions. 'W And now, turning to a 

 modern dictionary, we read : — 



' Sexagesimal arithmetic, a method of comj)utation by 

 sixties, as that which is used in dividing minutes into 

 seconds. — Sexagesimal fractions, fractions whose denomi- 

 nators proceed in the ratio of 60 ; the denominator is 60 

 or its multiple. These fractions are called also astronomical 

 fractions, because formerly there were no others used in 

 astronomical calculations. They are still retained in the 

 divisions of the circle, and of time, where the degree or 

 hour is divided into 60 minutes, the minutes into 60 

 seconds, and so on.'(^) 



Thus do the thought and practice of early man in the 

 Euphrates Valley still dominate the modern world. So 

 small is the sphere of invention and of original mental 

 effort ; so much easier is it to beg, borrow or steal. 



I pass on to notice two other Tablets, the first, 

 K. 90, details the monthly progress of the moon 

 through a circle of 480°; the second. Tab. 84-7-19, 

 273, details the same progress through a circle of 360°. 

 E. 90 has been more or less treated of by Lenormant 

 and by Messrs. Bosanquet and Sayce'^) ; and the 

 second Tab. by me in the Proceedings Soc. Bib. Archeeol., 

 Feb. 1900, where I give a copy of the remaining 

 part of it. The calculations of the moon's jirogress in 

 these two circles, although in some details at present 

 tinintelligible to me, are in perfect harmony. In the 

 circle of 360° the figures are, as they should be in order 

 to correspond, rtt lower. 



The two Tablets compare together thus : — 



Tablet A' 90. Tablet 84-7-19, 273. 

 (Circle 490°) (Circle 360°) 



80 60 = ^th of the 



•^^ — mouth and 



circle. 



Why the moon's apparent piice is thus varied is a 



question to which I invite the attention of astronomers. 



It does not concern the divisions of the circle. The first 



* Maspero, Dawn of Civilizaiion, Eng. edit. p. 773. 

 ' Imperial Diet, in roc. Sexagesimal. 



" Vide Bezold, Cat. of the Cun. Tabs, of the Kouyunjik Col. of the 

 Brit. Mus. i. 24. 



Tablet, written in 8umero-AkkiuIian, is of very high 

 antiquity; the second formed [)art of thi; great astrononiico- 

 astrological work The lllinnination of Bel,''* and therefore 

 belongs to the tliinl milliniium n.c. A circle of '.iiMP must 

 also be connected with a year of 360 days, and in another 

 TabletC*' the year is stated to lie composed of 12 months 

 and 360 days. In these circles of 360° and 480° the 

 numbers 6 and 60 are equally proniiment as in the smaller 

 circles. 



I will next notice how the circle-numbers become cycle- 

 numbers by the process of intensification already referred 

 to. My late friend Geo. Bertin, m one of his lectures on 

 Babylonian astronomy', stated that the Babylonians ' ad- 

 mitted the existence of a cosmical year. . . . This period 

 was one of ;5(;(i,()nO.' 1 have no original reference before 

 me, but the statements of the Greek writers are in thera- 

 •selves suflicient to show that Bertin was right. The 360° 

 of the circle multiplied by 10 = 3(Mt, which x 10 = :36,00(), 

 which X 10 = ;^60,000, a total the result of the principle of 

 triple intensification. The cosmical or divine year is thus 

 vastly greater than the human year. According to this 

 computation a divine day would =1000 years ; and this 

 reminds us of the familiar statement in our own Sacred 

 Books that, from the Divine standpoint, 'one day is as a 

 thousand years.' When, therefore, Epigenes of Byzantion 

 (tem. Augustus), who is stated to have studied in 

 Babylonia, declared <') that the Chaldisans had brick 

 records of astronomical observations extending over a 

 period of 720,000 years, these figures actually represent 

 2 cosmical years. The double of this, 1,440,000 or 4 

 cosmical years, is given by Simplikios'io) as the period of 

 these observations. Berosos and Kritodemos of Kos are 

 said*") to have put this term at 480,000 years, a number 

 arrived at by treating the circle of 480° in a similar 

 manner. Thus 480 x 10 x 10 x 10 = 480,000. 



It is to be further noticed that the Euphratean ideas 

 connected with cosmic periods appear to have influenced 

 other Asiatic nations. Thus, the zodiacal circle of 120° 

 X 10 x 10 = 12,000, reappears in the Iranian divine year 

 of 12,000 ordinary years, and which gives 1000 years for 

 each month and for each sign of the zodiac.*^-* Thus, 

 again, the Indian system of the Yugas or ages of the 

 world presents many features which most forcibly remind 

 us of the Euphratean scheme, and a Maha-yuga is 

 merely the Euphi-atean pieriod of 432,000 years intensified 

 by being multiplied by 10. Again, the Iranian stellar 

 host is said to be 6,480,000 in number,*'-" that is to sav, 

 4,320,000-f (5000 X 360 ( = 2,160,000), or 432,000 x 15, i.e., 

 the number of a Maha-yuga and a half of years. All 

 these numbers appear to be connected in origin, and are 

 in no instance arbitrary, the larger amounts being 

 intensifications of the smaller. 



Lastly, through the kindness of M. Clermont-Ganueau. 

 the eminent archaeologist, I can conclude with a notice of 

 a Palestinian cii'cle of late times, which shows most 

 strongly Euphratean influence, and in wliich by a very 

 peculiar arrangement are expressed, directly or indirectly, 

 circles of 12, 60, 120, 240 and 360 divisions or degrees. 

 M. Clermont-Ganneau says : — 



' Je me suis rappele un curieux monument que je me 



' Hence the remark of Pliny concerning Belus, ' Inventor hie 

 fuit sideralis scieutito ' {Hist. Nat. vi. 36). 

 » W. A. I. III. lii. No 3, Rev. 1. 6. 

 » Ap Pliny, Hist. Nat. vii. 36. 

 ' ° Ad Aristot. Peri Ouranou, 475 B. 

 ' ' Pliny, Hist. Nat. vii. 57. 

 ' '' Vide Bundahish, xxxiv. 

 '" Sundahish, ii. 6. 



