Focal Lines of Cylindrical Lenses. 81 



The table, fig. 18, shows the number and amount of 

 illumination of the image bands due to five object bands, the 





I 



\» 





G 





F 





£ 











C 





B\ 



A 





/ 





1 



! 



1 



'J' 



/ 





/ 



/ 



/ 



/ 



1 



1 



/ 



\ 



1 









2 



\ 



2 



2 



2 I 2 



2 





2 



2 



2 



2 



2 



\ 



2 









1 





1 





3 



\ 



3 



3 



3 





3 



3 



3 



\ 



3 





y 





I 









2 





2 





fj 



y 



4 





4- 



1 



4 





2 





2 



J 







1 



>J 



I 



2 



3 



'3 



5 



^ 



5 



5 



3" 



4 



3 



,3 



3 





; 





1 









2 





2 





■4 



/ 



4 





4 



f / 



4- 





2 



1 



2 









1 





1 





3 





3 



3 



3 





3 



3 



3 



J 



3 





/ 





/ 









2 



t 



2 



2 



2 



2 



2 





2 



2 



2 



2 



2 



y 



2 









1 



) 



I 



1 



/ 



I 



1 



/ 



J 





/ 



/ 



1 



/ 



/ 



/ 



/ 



) 



I 

















J 



r / 



G . 



/6\ 



















letters representing the same lines as in fig. 17 and the 

 numerals the number of slits which illuminate the particular 

 image bands ; for instance, i£ the image bands are formed at 

 some point between the lines B and there will appear to be 

 three bands illuminated from three slits separated by bands 

 illuminated from two slits, the edges of the screen beino* 

 illuminated from one slit. 



(2) The images of the vertical slits. 



Each point of each vertical 

 an axial and a tangential focal 

 the axial focal lines due to the 

 band will together form one 

 — u and v 2 be the distances of 

 lens the distance between the 



object band or slit will form 

 line. At the axial focus all 

 points on one vertical object 

 vertical image band, and if 

 object and image from the 

 vertical image bands will be 



= — -, and their width in 

 — u 



a horizontal direction will be 



WV2 



— u 



Consider now what will happen at the tangential 



focus. Every point on one of the vertical object bands will 

 form a tangential focal line of which the length will be 



= I 3 , v s being the distance of the line from the lens, h, 



Phil. Mag. S. 6. Vol. 20. No. 115. July 1910. G 



