CHAPTER V. METHODS OF PREPARING SECTIONS. Cutting and Grinding Machines.—Saws.—Cutting.—Grinding. Plates or Laps.—Cementing.—Grinding.—Mounting.—Cleaning and Finishing.—Convenient Apparatus for work. 117 CHAPTER VI. CHEMICAL AND MECHANICAL TESTS. Chemical Tests on Crystal in Section: _Carbonates_, _Gelatinizing Silica_.—Etched Figures.—Heating Section to Redness.—Methods of Isolating Crystals or Fragments for Testing: _Specific Gravity Separation_, _Electro-magnetic Separation_, _Chemical Separation_.—Micro-Chemical Reactions: _Borichy’s Method_, _Behren’s Method_, _Special Tests_. 129 APPENDIX. Brief Scheme of Classification into Systems by Optical Determinations.—Tables of Double Refraction (maximum) and Indices of Refraction (mean).—Diagram, showing relation between strength of double refraction, interference colors and thickness of section.—Order of Consolidation of the Constituent Minerals in Plutonic Rocks.—Optical Scheme with Special Introduction. 141 INDEX. 149 CONVENTIONS AND ABBREVIATIONS. a = The assumed direction of the ether vibrations of the fastest ray. b = The assumed direction of the ether vibrations of the ray with intermediate velocity. c = The assumed direction of the ether vibrations of the slowest ray. In some American Text-Books (by Iddings, Winchell & Phillips) a = X, b = Y and c = Z. a′ = The assumed direction of the ether vibrations of the faster ray in the given section.[1] c′ = The assumed direction of the ether vibrations of the slower ray in the given section. (+) = Optical character positive. (−) = Optical character negative. || = Parallel to. (γ − α) = The difference between the indices of refraction of the slowest and fastest rays, respectively, transmitted by the crystal, and indicates in decimals the relative strength of the double refraction. _n′_ = The mean index of refraction;[2] hence = (α + β + γ)/3 or (ε + 2ω)/3. α = Index of refraction of the fastest ray. γ = Index of refraction of the slowest ray. _a_, _b_ and _ć_ relate to the crystallographic axes commonly represented by these letters. 2_E_ = the apparent axial angle measured in air, 2_V_ being the true angle. _Bx_{a·}_ = The acute bisectrix. _Bx_{c·}_ = The obtuse bisectrix. _Ax. pl._ = The axial plane, _i. e._, the plane containing the two “optic axes.”