SOME EXPERIMENTA ON THE ZONAL ABERRATION OF LENSES. 757 



the 8 changes to a gamma form more or less distorted. If held further 

 away the lower half of the 8 becomes flattered into a delta. 



Paradox D. 



The sliaclow of a horizontal line is a triangle. The disposition of the 

 apparatus remaming as last mentioned, if the horizontal object is 

 moved further to about 212 centimètres away from the lens, and at a 

 slightly lower level, the upper part of the 8 vanishes leaving a simple 

 delta-shaped line, or hollow triangle, as the shadow of the object. 



The whole of thèse paradoxical effects can be shown by the use of 

 any plano-convex lens. The modifications which occur when other 

 lenses, biconvex and meniscus, are used, have also been studied. To 

 describe them here would undnly prolong tliis communication. Paradox 

 A was shown, along with some of the earlier experiments,to the Physi- 

 cal Society of London at its meeting on November 13 th , 1899. It is to 

 be hoped that physicists may turn their attention to the study of this 

 neglected branch of geometrical optics, and will further investigate the 

 properties of non-homocentric pencils of rays. 



London, September 26 th , 1901. 



