748 



SILVANUS P. THOMPSON. 



the lens-system must be corrected to fulfil a third condition, when the 



The aberration commonly called ^spherical 11 and that termed ^zonal 11 , 

 are both due to the unequal performance of the zones of the lens. A 

 simple considération will elucidate the différence between them and will 

 also show that in the case of a simple lens having but two refracting 

 surfaces^ thougli either kind of aberration may be reduced to a minimum 

 by a suitable choice of curvature for the surfaces, they cannot both be 

 simultaneously eliminated since the conditions for eliminating the one 

 are in conflict with thèse for eliminating the other. 



To eliminate central aberration (the „spherical aberration 1 '' of the 

 text-books) as is necessary in télescopes, it is requisite to fashion the 

 lens so that the apparent principal focal lengtli, as measured from the 

 back pôle or vertex of the lens to the principal focus, shall be the same 

 for ail zones. To eliminate zonal aberration, it is requisite so to fashion 

 the lens that the true focal length shall be the same for ail zones; since 

 the magnifying power dépends on the true focal length and not upon 

 the apparent focal length. As is well-known two lenses may have their 

 respective principal foci at equal distances from the back surface of the 

 lenses, and yet those two lenses may magnify quite differently. In the 

 theory of Gauss which deals with the properties of an idéal lens, never 

 realized in practice, tins différence in magnifying power between two 

 lenses that have the same apparent focal length is explained by a geo- 



Jjl £- 1m and called a prin- 



cipal plane (LTaupt Ebene). In the theory of Gauss the true focal 

 length is the distance of the principal focus from tins principal plane. 



system becomes anastigmatic. 



F 3 ç fJo 



metrical artifice ; 

 the refraction exer- 

 ted by the lens 

 upon a given ray 

 parallel to the prin- 

 cipal axis being re- 

 ferred back to an 

 imaginary surface, 

 which in Gauss' s 

 theory isconsidered 

 always as a plane 



