272 M. I. Goldman — Catahoula Sandstone of Texas. 



quartz grain smaller than this could be rounded. His words 

 are : " any finer-grained sand would doubtless^ be angular." 

 Ziegler* too, after some rather unconvincing experiments, him- 

 self does not dare say more than that " In view of the results 

 it seems improbable\ to the writer that grains less than 0'75 mm 

 in diameter could be well rounded under water." Strong 

 evidence, however, that this conclusion is wrong is afforded by 

 the observations of Worthf in the English Channel, where he 

 found well-rounded grains of 0*5 mm or less that had almost 

 certainly been rounded by strong wave action. 



As to the ratio of the lower limit of rounding in air to 

 rounding in water, Mackie,§ from theoretical considerations in 

 which, in addition to the factors enumerated above, the veloc- 

 ity of the grains is also taken into account, deduces that for 

 wind at 8 miles an hour the lower limit of rounding will be 

 one-fifth that for water at 2 miles an hour, but only for these 

 two velocities. Since winds of much greater velocity are 

 known, it would appear, if we accept even Ziegler's limit of 

 0'75 mm for water, that the most minute grains might be rounded 

 by wind. But Udden| draws attention to the fact that the 

 lower layer of the air, which acts directly on the surface mate- 

 rial, is so much affected by friction that its velocity increases 

 very slowly with increase in the velocity of the free wind (he 

 thinks it probably never reaches three miles an hour). 



From actual observations on the lower limit of rounding 

 of sands in nature, the only figures I could find were in Friih's 

 paper on loess.^f As an absolutely definite figure he gives 

 0'034 mm diameter (sample 11) for a rounded grain in Pampas 

 soil. Less definite figures are given for analyses 2 and 8 

 (European loess), which he states have rounded grains in 

 material between 0'019 and O06 mm , and O'Ol to O'Oh^ diame- 

 ter respectively ; but that the smallest grains included in these 

 sizes showed rounding is not stated, so that we must be satis- 

 fied with O034 mru . However, this is exactly the diameter of 

 the smallest well-rounded grain that I found in the Catahoula 

 sandstone. Now Friih's samples are distinctly considered 

 seolian, so that while we have for comparison no figures as to 

 the lower limit of rounding in water-borne material, the fact 

 that 0-034 mm is the diameter of the smallest rounded grain 



* Ziegler, Victor : Factors influencing the rounding of sand grains, Jour, 

 of Geol.,xix, p. 654, 1911. 



f Allen E. J., and Worth, E. H. : On the fauna and bottom deposits, etc., 

 Jr. Marine Biol. Assoc, Plymouth, England. N. S., v, p. 385, 1899. 



\ Italics are mine. 



§ Mackie, Win. : On the laws that govern the rounding of particles of sand, 

 Trans. Edinb. Geol. Soc, vii, p. 310, 1897. 



||Udden, loc. cit., p. 23-24. 



If Friih : Der postglacialle Loess in St. Gallen, etc. Vierteljahreschrift 

 naturf. Ges. Zurich, xliv, pp. 174-5, 1899. 



