The wave-length of a middle color may be taken as 560 μμ (millionths of a millimeter); hence each quarter undulation mica plate may be considered to possess a phase difference or retardation of 140 μμ. If, then, between the polarizer and analyzer we insert the mica wedge, so that its direction of vibration of the slower ray, _c_, is at right angles to that of the mineral under examination, we subtract from the phase difference of the mineral an amount equal to _n_ times 140 μμ, in which _n_ represents the number of superposed mica plates in the field. When the mineral appears dark the value evidently corresponds closely to the phase difference of the mineral.[62] From the expression Δ = _eX_, in which Δ is the phase difference or retardation, _X_ the double refraction, and _e_ the thickness in millionths of millimeters, the thickness can be deduced when the double refraction is known or _vice versa_. If a mineral of known double refraction can be found in the section near the mineral under investigation,[63] the double refraction of the latter can be deduced by measuring the phase difference of the known mineral, whence e results, and this substituted in the above formula yields _X_.” METHOD OF DETERMINING MINERALS AND THICKNESS OF SECTION, BY USE OF TABLE OF DOUBLE REFRACTION (MAXIMUM) AND DIAGRAM.[64] Select some easily recognized mineral in the rock section and note the maximum interference color given by any of its sections.[65] The strength of the double refraction of this mineral being known, look up on the diagram the diagonal line corresponding to this double refraction and follow along this line toward the left hand lower corner until the observed interference color is reached, when the horizontal line will indicate the thickness of the section. The thickness is given in hundredths of millimeters. Then in the case of the unknown mineral pick out the section giving the highest interference color and carry along the same horizontal line until this new color is located,[66] then pass up to the right along the diagonal line to the numbers indicating the strength of the double refraction of the unknown mineral. Turn to the table where the minerals will be found having about this strength of double refraction.