. Physiological optics : being an essay contributed to the American encyclopedia of ophthalmology . of this equation is to lie with its axis at the angular posi-tion indicated by 8; if the solution of the equation gives a negativevalue to the angle 8, cylinder B lies at that angle. In addition, complications will be avoided when the two cylindersat oblique axes have different signs if they are transposed first of allinto an equivalent sphere combined with the two cylinders whichshould now have the same algebraic signs but one of the axes changedby 90°. An illustrative case will show the operat
. Physiological optics : being an essay contributed to the American encyclopedia of ophthalmology . of this equation is to lie with its axis at the angular posi-tion indicated by 8; if the solution of the equation gives a negativevalue to the angle 8, cylinder B lies at that angle. In addition, complications will be avoided when the two cylindersat oblique axes have different signs if they are transposed first of allinto an equivalent sphere combined with the two cylinders whichshould now have the same algebraic signs but one of the axes changedby 90°. An illustrative case will show the operative and mathematical pro-cedure. 0. D., stenopaic slit used; slit position at 55°, vision sharpest; 151 PHYSIOLOGICAL OPTICS slit position 165, vision poorest, -f 2D. S., slit at 55°, gave V = 8/10and —4 D. S., slit at 165, produced V = %0. The prescription as adouble cylinder at oblique axis is, then, -(-2 cyl. ax. 145° 3 — ax. 75°. The angles 6lt 02 and y are known; they are 145°, 75° \ Tq find Angle between Horizontal and one Cross CylinderVERTICAL LINES; d„ord2,or D2-D,. KEY TO SYMBOLS d, and d^ PWers of oblique cylinders.£! andO^Angtes corresponding to oblique £le between oblique cylinders =0z-9,D, and D2=,Reguired powers of cross ;f= Required ari^le from horizontal to D|. C = Quantities required in determining <?. I- To find D, and D^: Fmd value of d*d2 in scale at topand move vertically downward to intersectobliqueline for angle T= oblique cylindersMove left to dividing line and downward to point on hor-izontal line through d+d1 as indicated in scale at left FindD. and D2from nearest oblique line, interpolating if desired torclose results. If value of d,+d2 is minus, frombroken or dotted oblique lines opposite d. + di,as in Example Ztin which D, is minus and D2 plus. Il-Angles indicated by oblique lines. G, is found on horizontal line intersecting verticalthrough d, and oblique line for 6;. C
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