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 



