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668 DEMONSTRATING REFRACTIVE EYE DEFECTS [Cn. XV
With the vertical lines in focus, add another convex cylinder of 0.5 diopter and arrange the axes of the two cylinders at right angles (cross the cylinders). All the lines will now be sharp, for the added convex cylinder increases the curvature where it was lacking, and thus gives the combination a symmetrical curvature. It is to be noted that when convex cylinders are crossed in this way they add to the original lens the dioptry of the cylinders. In this case 0.5 diopter, and the image is increased in size (fig. 389 C).
Two concave cylinders can be used in the same way, but with concave cylinders the entire system is reduced in dioptry the amount of the cylinders. In this case it would reduce the dioptry half a diopter and hence the image would be smaller (fig. 389 B).
§ 930. Correction of astigmatism by the obliquity of the spectacles. — It was pointed out by Young (1800), that astigmatism might be corrected by making the spectacles sufficiently oblique to neutralize the defect. This can be demonstrated very strikingly as follows :
Use the same outfit as in § 927. Make the image of the radial lines sharp on the screen and add the +0.5 diopter cylinder with the axis vertical (fig. 390). Now put a convex lens of i diopter in front of the cylinder and focus for the lines parallel to the axis of the cylinder (vertical in this case). Tip the convex lens up or down, i. e., across the axis of the cylinder, and when the right obliquity is reached the lines will all be sharp. This is because the tipped lens introduces the curvature lacking in the cylinder. This can be shown by removing the cylinder and the horizontal lines will be sharp showing that the vertical meridian is unchanged but the horizontal meridian has been increased in curvature.
Use the same cylinder but a concave lens of i diopter instead of the convex lens ; focus the combination until the horizontal lines are sharp, then rotate the concave lens sidewise (i. e., parallel with the axis of the cylinder), and when at the right obliquity the radial lines will all be sharp. This is because the oblique, concave lens neutralizes the greater curvature of the +0.5 cylinder. In a word, the oblique position of the spectacle makes it act like a cylinder in