754 



SILVANUS P. THOMPSON. 



or by varying, by means of an interposée! condenser, the divergence of 

 the incident pencil various modifications are obtained in the détails of 

 the successive forms of the coma ; or of the zone-images if a zone plate 

 is applied to the lens. 



Experiment 4. On reversing the lens, so that its curved face is pre- 

 sented to the lamp, so as to obtain an inwardly-pointing coma, a similar 

 séries of successive forms is obtained upon the screen, but again with 

 modifications; the principal différence being that, (for a like conver- 

 gence of the incident pencil and for an equal obliquity of the lens) the 

 point where the most distorted part of the annulus cusps upwards and 

 crosses itself, lies within instead of without the less-distorted part of the 

 aûnulus. 



Steinheil, by a laborious use of the trigonometrical formulae for 

 rays that do not lie in any axial plane of the lens, has calculated out l ) 

 the aberration figures for the objective of the celebrated Kônigsberg 

 Heliometer. Thèse calculated figures very closely resemble some of the 

 séries of Fig. 4. The theory of the non-homocentric beam which gives 

 rise to them has been developed by S. Finsterwalder in his remarkable 

 memoir entitled: Die von optischen Systemen grôsserer Oeffnung und 

 grosserer Gesichtsfeldes erzeugten Bilder. 2 ) 



Experiment 5. The pencil of rays which have traversed the oblique 

 lens is no longer homocentric. In conséquence of this fact some very 

 extraordinary phenomena appear, when objects indroduced into this 

 beam are caused to cast their shadows upon a white screen. Thèse 

 results are best stated in the form of paradoxes. 



Paradox A. 



The shadow of a horizontal line is a ring. To obtain this resuit the 

 lens is placed about 90 centimètres from the luminous point, and the 

 lens with its fiât face turned toward the light is tilted about 25° as in 



*) Sitzungs-Berichte der math.-phys. Classe der k. bayerischen Akademie der 

 Wissenschaften, 1889, Bd. XIX. 



2 ) Abhandlungen d. II Classe d. k. Akad. d. Wissenschaften in Miinchen, 

 Bd. III, p. 519. 



