THE PERCENTAGE COMPOSITIONS OF ROCKS 285 



IV. CASE OF SPHERES CLOSELY PACKED AND SQUEEZED TOGETHER 



When spheres are closely packed and are then squeezed 



together they tend to assume the form of dodecahedrons. 



A cross-section through such a mass will give a series of triangles. 



hh 

 If h is the base of such a triangle and h its height, its area is — . 



Nbh wiU be the area of the sum of such triangles and the ratio to 



Nhh 

 the whole, -j^ . Since every parallel section will give an equal 



distribution of light and dark, the volume of dark mineral will 

 be DNhh and its ratio to the whole -yr^ — , which is the same per- 

 centage ratio as in the case of the surface measurement. 



Thus, no matter what the shape of the individual mineral 

 grains, if they are uniformly distributed the surface ratios are 

 exactly the same as are the volume ratios; consequently surface 

 measurements may be used to represent volume measurements in 

 the determination of the composition of a rock. 



