THE PHYSICAL PROPERTIES OF SOILS 53 



If the spheres were arranged in the form of a pyramid, 

 like a pile of cannon balls (Fig. 7), they would lie much 

 closer together, the points of contact would be more 

 numerous, and a larger number would be required to fill 

 a given volume. In such a case the spheres would occupy 

 74*1 per cent, of the total volume, and only 25'9 per cent, 

 would be left unoccupied. 



This explains why the volume of a loose powder is per- 

 ceptibly diminished on shaking and how a soil may be 

 consolidated by pressure. The particles undergo re- 

 arrangement; they are brought into closer contact and 

 the amount of interstitial space is reduced. 



The size of the particles, so long as they are uniform, 

 does not affect the relative proportions of occupied and un- 

 occupied space. If the particles were smaller so also would 

 be the spaces between, but as there would be more of them 

 the total amount of occupied and unoccupied space would 

 remain unaltered. Thus, if the diameter of the particles 

 were divided by a there would be a 3 times the number in 

 the same volume, and the space occupied by them would b 

 the same. 1 This may, perhaps, be made more plain by 

 supposing the mass of particles to be viewed through a 

 magnifying glass. The particles and the spaces would be 

 magnified in the same proportion, but the relation of one 

 to the other would not be affected. 



It is obvious that smaller particles could be introduced 

 into the interspaces, and the amount of unoccupied space 

 could be thus considerably reduced. Variation in the size 

 of the particles therefore tends to reduce the amount of 

 unoccupied space. Particles of irregular shape, like those 

 of soils, could be arranged more closely than spheres, but 

 not so closely as cubes. Any adaptability of shape due to 

 softness of the particles would also tend to reduce the 



4/3 TT (r/a)3 = * ~ = 4/3 IT r". 



