the Spherical Aberration in a Lens-System. 



91 



The rest of the numerical work may be arranged as 

 follows : — 









+ 



— 



2nd order j f^®' 



= 



•002,844 





corrections 1 i 



= 



•002,960 







•005,804 







r 6-ft 



= 



•000,341 









= 



•000,022 







t»^*@+s>) 



= 



•000,076 







S*^*(s + i) 



== 





•000,353 



3rd order 

 corrections 





= 





•000,303 



_ 2 y»V A '» /* A 'A 



r 2 V # 3 «2 3 / 



= 



•000,234 







3 .A> 

 2 yi V 4 



= 



•000,076 







3 /A' 2 _^A 



= 



•000,489 









= 





•000,101 







= 





•000,082 





•007,042 



•000,839 









•000,839 





+ •006,203 



To get the final value o£ A 2 this must be multiplied by 



— 2 or 16. This gives +'099,248. 



An accurate tracing of the extreme ray through this lens 

 by a trigonometrical method gave for the longitudinal 

 aberration +'099,37, showing a negligible discrepancy or 

 •00012 approximately, 



Feb. 3, 1910. 



