Astigmatic Aberration. 527 



This simple formula 0= constan t expresses in a most con- 

 venient form the general equation^ for any ray of a synnne- 

 trical astigmatic beam, and exemplifies for such a ray the 

 property which causes the twisted effects observed in "^con- 

 nexion with astigmatic beams. 



It is obvious since 7=(tcos</) and e^h sin that in con- 

 structing a string model of the astigmatic surface, points in 

 the focal lines that correspond and that can be connected bv 



a string are points with a phase-difference of ^ in harmonic 

 oscillations along the focal lines. '"" 



To investigate the shadow produced by an object placed in 

 an astigmatic beam, such as has been dealt" with above, 

 let the receiving screen SS' be beyond the secondary focal 



line at a distance s from the plane X Y. Then the 

 QPP^R, or 01, will intersect the screen SS' in a point i, 

 coordinates of which are 



ray 

 the 



j'^'^-C^^)^' 



y= 



S 6 



2 = S, 



