EROSION BY RIVERS 253 



Rounding of Saud Grains. (Goodchild-27 ; Mackie-47 : joo.) 

 The chief factors concerned in the rounding of sand grains by 

 attrition are : 



1. The size of the particles. 



2. Their specific gravity. 



3. Their hardness. 



4. The distance over which they had traveled. 



5. The agent by which they had been transported. 



The amount of rounding of a particle varies directly as i, 2 and 

 4, and indirectly as 3. Particles transported by wind are more 

 rounded than those transported an equal distance by water. 



A cube, with the side measuring i inch, presents an area of 6 

 square inches, while a sphere of one inch diameter presents a sur- 

 face of only 3. 141 59 -|- square inches. Now, since the surface area 

 of bodies of similar figure, but different in size, varies as the square 

 of their linear dimensions, a doubling of the linear dimensions of 

 the cube would increase its surface area to 24 square inches. If 

 the diameter of the sphere is doubled, the surface area becomes 

 12.566 4- square inches. On the other hand, reducing the cube 

 from a linear dimension of one inch to one of half an inch by the 

 side, the area of its surface is reduced from 6 square inches to one 

 and one-half square inches. In like manner the reduction of the 

 diameter of the sphere to one-half inch reduces its surface area to 

 0.78539 square inch. 



The volumes of bodies of similar figure, however, increase as 

 the cube of their respective linear dimensions, or decrease as the 

 cube root of those dimensions. Thus, while the sphere reduced 

 from one inch to one-half inch diameter changes in area from 

 3.1416 square inches to 0.78539 square inch, its volume will change 

 from 0.5236 cubic inch to 0.06545 cubic inch. That is. while 

 the superficial area is decreased to one-fourth, the volume is de- 

 creased to one-eighth its original amount. Since the weight of an 

 object depends on its volume, it follows that the decrease in weight 

 is greater than the decrease in surficial area, and, since adhesion 

 (surface tension or the adhesion between the object and the medium 

 in which it is immersed) is dependent on the surficial area of the 

 object, it follows that in the wearing down of a sand grain the de- 

 crease in weight is always greater than the decrease of surface ten- 

 sion. Thus, with the progressive wearing down of a sand grain, a 

 stage will be reached when the surface tension will balance the 

 gravitational force, and further wearing of the grain becomes im- 

 possible in that medium. So, with a given medium and strength 



