SOME EXPERIMENTS ON THE ZONAL ABERRATION OF LENSES 



BY 



SILVANUS P. THOMPSON. 



"When an oblique pencil of light passes obliquelj through a lens 

 certain unilatéral phenoînena of aberration are observée!. Let it be 

 assumée! tliat there are no chromatic aberrations, or, wliat amounts to 

 the same thing, tliat tbe light employée! is mono chromatic. Then, in 

 gênerai there will still be several kinds of aberration présent. Even if 

 the lens-system be such as to be corrected for spherical aberration 

 for a principal parallel beam of light (Euleu's condition) so that 

 ail its several zones agrée in having one common point as their 

 principal focus, the lens will nevertheless possess aberrations for obli- 

 que pencils, and for pencils proceeding from points on the principal 

 axis at finite distances from the lens. The focal spot, for such an obli- 

 que beam or pencil, is no longer a point; it is distorted ioto an oval- 

 shaped, spindle-shaped, or comet-shaped patch, having a well-defmed 

 edge but very unequally illuminated. As is known, tins phenomenon, 

 called Coma, arises from a spécial zonal aberration of another kind, due 

 to the several zones of the lens having différent focal lengths and not 

 fulfilling the sine-condition *) as elefineel by Abbe. If a lens lias been 

 corrected for central aberration (Euler's condition), and also for zonal 

 aberration (Abbe's condition), then, as von Seidel bas shown 2 ), it will 

 exhibit, for oblique pencils, a pure astigmatism, giving two well-defined 

 focal lines, one tangential and one radial in direction, situated respec- 

 tively on the first and second focal surfaces which both eut the principal 

 axis at the principal focus. To reunite thèse focal lines in a focal point 



*) Archiv. fur mikrosk. Anatomie; Bd. IX, pag. 420, 1873. 

 2 ) Astronomische Nachrichten, Nos. 1027 to 1029, April 1855; and Sitzungs- 

 berichte der k. bayrischen Akademie, 1898, p. 395. 



