February 



1908J 



NA TURE 



347 



" No mere description," says Ihe author, " can 

 convey an adequate idea of the grandeur of the 

 country between Belvedere and Blyde River Poort, 

 where this stream enters the granitic Low Veld 

 ;irea." The escarpment of the Dracl-censberg "here 

 forms a fine semi-circular curve, cut into by a num- 

 ber of spruits which give rise to precipitous and 

 densely wooded kloofs. Immediately below the edge 

 of this escarpment runs a massive kranz of quartzite 

 nearly 500 feet in thickness." About a thousand feet 

 b;-low lies the great plain of the Low Country, beyond 

 which, on a clear day, the distant chain of the 

 Lebombo Hills can be discerned. The dip of the Black 

 Reef Series being to the w^est, the escarpment rises 

 eastward until it culminates in two magnificent bluffs, 

 ',500 feet higher than the Belvedere (see Fig.). North 

 of Belvedere the greater thickness of the quartzites 

 produces, under the profound erosive action of the 



Portion of the Great Kast<;ni Escarpment of the Drakensberg. S. of 

 Belvedere, fojmed by the Black Reef Series. 



larger rivers, even more striking scenic effects. Thus 

 the Blyde River is mentioned as having carved out 

 a canon in the qu.irtzites to a depth of more than 

 2000 feet. 



The Dolomite, owing to its more homogeneous com- 

 position and consequent absence of marked hori- 

 zontal features, is characterised by a different type of 

 scenery. Its vertical jointing, however, gives rise to 

 peculiarly pointed kopjes, recalling portions of the 

 dolomite area in the Tyrol. Northward, from Pil- 

 grim's Rest to Hermansbufg, the Blyde River flows 

 in a gorge formed by precipitous walls of dolomite. 

 It then travels in a more open valley; but on leaving 

 the Dolomite it cuts its bed down into the Black Reef 

 quartzites by a succession of cataracts and water- 

 falls until, joining forces with the Treuer River and 

 the Belvedere Creek, it forms the deep canon men- 

 tioned above. 



NO. iqqS, vol. 77] 



The Pretoria Series presents in the Lydenburg dis- 

 trict no feature, either topographical or geological, 

 of especial interest; the same succession of shales, 

 quartzites, and intrusive sheets is met with as in the 

 country further south. The only noteworthy point is 

 the marked thinning out of the series which is ob- 

 servable to the north of Lydenburg. The middle 

 member of the system — the Dolomite — undergoes no- 

 great change in thickness, although a thick bed of 

 quartzite (the " Blyde Quartzites ") makes its appear- 

 ance for the first time in the middle of the series ; but 

 while the upper member — the Pretoria Series — be- 

 comes much attenuated, the lower member — the Black 

 Reef Series — rapidly assumes greater and greater 

 proportions as it is traced northwards. In the extreme 

 eastern portions of the Rand basin, near Springs, the 

 boreholes put down through the Karroo Coal-measures 

 and the Dolomite, to cut the underlying VVItwaters- 

 rand Beds, showed that the Black Reef Series was 

 represented at the base of the Dolomite by a bed of 

 hard quartzite only 20 feet in thickness (see Haicn, 

 Trans, of the Geol. .Soc. of S. Africa, vol. vii., 1904, 

 p. 63). At the Devil's Kantoor, in the Barberton dis- 

 trict, it is no feet thick; at Mac-Mac, 700 feet; at 

 Belvedere, 1260 feet ; while near the northern ter- 

 mination of the Drackensberg, at.Marieps Kop, the 

 series reaches 2550 feet. The horizontal distance 

 across the syncline formed by the beds of the Transvaal 

 System, under the Waterberg and Red Granite for- 

 mations, from Springs to the Drackensberg escarp- 

 ment, is only about i6o miles, so that the conditions of 

 sedimentation must have changed rather rapidly, the 

 cause of which is not explained. 



It will be seen by the free use made of Boer topo- 

 graphical words in the sentence quoted above that 

 the committee appointed by the British Association 

 at its last meeting " to determine the precise 

 significance of topographical and geological terms 

 used locally in South Africa " should serve a useful 

 purpose. The precise meaning of such words as 

 kranz, biilt, vlei, and Jdoof will not be known to the 

 generality of English readers, although kopje, veld, 

 ind spruit may have been made familiar by the late 

 war. The report is accompanied by excellent colour- 

 printed maps, and illustrated by beautiful photographic 

 reproductions; but, unfortunately, it lacks an index, 

 and has not even a paged table of contents. 



F. H. Hatch. 



THE HISTORY OF ARITHMETICAL 

 NOTATION. 

 'X'HE invention of the decimal notation, which in- 

 -*■ volves the use of zero and the assignment of 

 local value to digits, made such an immense alter- 

 ation in the character of arithmetical calculations that 

 it would be extremely interesting to know its origin. 

 It became familiar in Europe mainly through Moham- 

 medan sources ; hence the term Arabic, as opposed to 

 Roman notation. But the discovery of Sanskrit liter- 

 ature and of Indian \vorks on mathematics led to the 

 theory that the real inventors of the system were the 

 Hindus. The object of Mr. Kaye, in the paper re- 

 ferred to below,' is to show that this conclusion has 

 been based on insufficient evidence, and that the whole 

 question requires further and more careful consider- 

 ation, including a critical study of Indian texts, to 

 avoid being misled by spurious documents. Mr. 

 Kaye gives in the first place a series of arguments 

 which go far to prove that there is no trustworthy 

 evidence for the use of the new notation in India 



Kaye. (Jo 



'1907.) 



Indian Mathemalicf. — Arithmetical Notation.' 

 nd Proc. As. Soc. of Bengal, new series, vol. 



By R. 



