THIRD HYPOTHESIS OF DERIVATION 463 



If a plane of cross-section perpendicular to the schist plane runs also 

 normal to the fibration, the short plates so obtained are always of di- 

 minished value, in calculation of areal proportion of minerals — linear 

 and smallest of all where the planes of the blades lie in the schist plane. 



If the same section plane runs parallel to the fibration, through par- 

 allel blades whose planes are irregularly disposed, the proportionate 

 areal value may be excessive, as found on the schist plane. With planes 

 of the blades in the schist plane, their sections are linear and their areal 

 value too small. 



If the axes of blades are divergent and their planes in the schist plane, 

 or, it may be, irregularly disposed toward it, an estimate of their predom- 

 inant orientation needs to be made to determine whether the conditions 

 approach more closely to those of A, B, or C. 



Ordinarily a section of the rock may be sliced at such an angle to the 

 schist plane and to the fibration that the plates or sections of the blades 

 in the new thin-section may present an average area, a' (= d'^), in ap- 

 proximately correct proportion to the volume of the mineral in the rock 

 intermixture. The more oblique the section plane, the larger, of course, 

 the area of plates so obtained. 



Section plane 



Figure 4. — Diagram showing proper Section Plane inclineb to Fibration, in thick Blades. 



B. Schists of irregular texture, made up of prisms, thick blades, 

 needles, or fibers of the predominant mineral, with approximately square 

 cross-section, and with the other minerals in intervening laminae of un- 

 equal or greater thickness. For a rock of this kind a thin-section might be 

 sliced in some cases obliquely to the schist plane, as in C ; but it may be 

 generally preferable, from easier manipulation, to prepare a section normal 

 to the schist plane, inclined obliquely to the direction of fibration, in the 



manner illustrated in figure 4. Then — =^l' ', that is, if the average area, 



a' (== d'"^) of the plates of the predominant mineral required in proper 

 cross-section, ascertained by the method explained before, be divided by 

 the known thickness of the blades, we obtain the length of the plates {}') 

 required in the proper cross-section. The actual average length of the 

 plates on the schist plane being known (/). we have for the small triangle 



above on that plane the formula j, = sin A' ; that is, the sine of the 



