484 



tillyer: variation of equivalent focus 



distant from the center. Near the axis it is almost impossible to 

 obtain an accurate value of either AE or A ?; and the problem be- 

 comes physically indeterminate. 



This method was first tried upon a telescope objective of 320 

 mm. equivalent focus, the trigonometric residuals of which were 

 already known. 



TABLE 1 



Telescope Objective, E = 320, X = 0.55 ju- Residuals in Hundredths of a 



Millimeter 



From these residuals it is seen that the probable error of a 

 determination near the edge of the objective is only a few hun- 

 dreths of a millimeter. Moreover it is evident that this objec- 

 tive is exceptionally well made. 



The results of measurement of the spherical aberration and 

 departure from the sine condition for three photographic objec- 

 tives are plotted in figure 2. Curves A and B were made from 

 high speed anastigmats with an aperture ratio of about F 3.5 

 while curve C is an older much used type of symetrical anastigmat 

 having an aperture ratio of about F 7.7. One pecuUar feature of 

 curve B is the difficulty experienced in determining the relative 

 positions of the zero values of E and v, the v curve apparently 

 having a point of inflection near the axis. This may be due' to a 

 small error in grinding the surface, to an error in the measurements, 

 or to a true aberration in this type of lens. Some evidence exists 

 that this is a true aberration since the actual coma found in this 

 lens changes sign at only a small angle with the axis. Both 

 lenses, however, are remarkable for their freedom from aberra- 

 tions and for the care taken in their construction. ' 



