THE ROUNDING OF SAND GRAINS 651 



Summary of previous work. — McKee in his work evolves the 

 formula 



size X specific gravity X distance traveled 



Rcc 



hardness 



where R is the rounding (or the wear) . 



Considering a cube with the edge x, the distance traveled 

 would be roughly proportionate to the number of times the grain 



turned over, hence -- could be placed instead of distance. The 



4X 



weight of the cube would be x 3 Sp. Gr. 



Substituting in the above equation we have 



x 3 Sp. Gr. — 



hardness 



reducing to 



„ x 2 Sp. Gr. d 



R<X : 



\h 



Or in more general terms — 



x 2 Sp. Gr. d 



Rv. 



mh 



where m is a constant depending on the shape of the grain, m 

 is 4 in the case of a cube, 3 . 141 6 in the case of a sphere, etc. If 

 the grain is under water allowance must be made and 



_ x 2 • (Sp. Gr. — 1) • d 



A a ; 



mh 



Goodchild goes farther and determines a general limiting con- 

 dition to the wear taking place. His work may be summarized 

 as follows : 



Since the sand is completely surrounded by a film of the water 

 in which it is submerged, it will be acted on by surface tension. 

 By decreasing the size of a particle we increase the ratio of area 

 to volume, and hence to weight. Since the surface tension of 

 water will act over the area exposed, its magnitude compared to 

 the weight of the grain will increase with decrease in size. Finally, 

 he assumes that a balance between weight and surface tension 

 will be reached, such that no further rupture of the film of water 

 surrounding the grain can take place, and hence all wear will 



