668 DEMONSTRATING REFRACTIVE EYE DEFECTS [Ch. XV
With the vertical lines in focus, add another convex cylinder of
o-s 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 1 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 1 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