284 Dr. G. J. Burch. Some Uses of Cylindrical [Feb. 29, 



being removed, the second is inserted in the other cell and adjusted to 

 focus the vertical line. 



The first lens is then replaced in position and rotated till both lines 

 are sharply focussed. When three lenses are used, the two employed 

 to obtain magnification must be contained in a sliding tube furnished 

 with a pin working in a slot to prevent rotation. 



In the preceding pages the axes of curvature of the two components 

 of the cylindrical lens-systems are, in all cases, at right angles to each 

 other. Equally interesting properties are possessed by those systems 

 in which they are parallel to each other. 



Case L — Two equal convex cylindrical lenses set with their axes of 

 curvature parallel, and at such a distance apart that their principal 

 foci coincide as in a telescope. 



A clear and undistorted view of distant objects is obtained, but on 

 rotating the object the image appears to rotate with equal angular 

 velocity in the opposite direction, and on rotating the tube containing 

 the lenses, the image appears to rotate with twice the angular velocity 

 in the same direction. 



The reason is obvious. Suppose the axes of curvature are vertical, 

 ^hen there is no vertical deviation of the image-forming rays, and so 

 far as its vertical components are concerned the virtual image coincides 

 with the real object. In the horizontal plane there is deviation. The 

 rays from the cylindrical objective cross as in a telescope before 

 reaching the cylindrical eyepiece. If, therefore, we focus the eyepiece 

 so that the final virtual image is at the same distance from the eye as 

 the real object, a clearly defined image will be produced, erect, but 

 ^nantiomorphic, as if reflected in a plane mirror. If the object is 

 viewed through two cylindrical telescopes in tandem, then if either is 

 rotated, the image rotates in the opposite direction, but if both are 

 rotated together, the image remains stationary as in the case of two 

 •erecting prisms in tandem. 



Two causes may disturb the sharpness of the definition, namely, 

 deviation from exact parallelism of the axis, and error in adjusting the 

 distances between the lenses, so that the horizontal components of the 

 virtual image are not focussed at the same distance as the vertical. 



If the two lenses are not of equal focal length the resulting images 

 are clearly defined, but not symmetrical, being magnified or diminished 

 in one direction and of natural size in the other. 



Case II. — Two cylindrical lenses with their axes of curvature parallel, 

 the distance between them being greater than the sum of their focal 

 lengths. 



Such a system acts as a compound microscope, giving well defined 

 images of objects situated at a certain distance from the objective. 



