Vol. IX] WOODWORTH— OPTICS OF THE MICROSCOPE 187 



The differences just painted out have not been wholly- 

 unknown to physicists by any means, but apparently it has 

 not been made clear that the differences are due to fundamental 

 laws of focus formation equally applicable to narrow as well 

 as wide bundles of rays. 



III. Oblique Axis Calculations 



The system of lens calculation proposed by the writer con- 

 sists of the calculation of a definite series of rays throug-h an 

 optical system, either graphically or mathematically, and in 

 the latter case the plotting of these rays on an enlarged drawing 

 of the lenses. When this is done a simple inspection of the 

 drawing will enable one to estimate the simultaneous effect 

 upon the aberrations of any possible variation in the construc- 

 tion data. 



The rays that need be calculated are as follows : 



1. The Zone ray, commonly called the edge ray, the ex- 

 treme ray from the point of intersection of the optical axis 

 and the object. This ray determines the aperture of the in- 

 strument. 



2. The Field ray from the extreme edge of the field 

 midway between the extreme rays of the pencil. This ray de- 

 termines the magnification of the instrument. 



3. The Paraxial ray from the object along the optical 

 axis. The difference between this and the Zone ray, measured 

 on the X axis, determines the axial aberration, that between 

 this and the field ray also measured on the X axis determines 

 the curvature. 



4. The Distortion ray similar to the Field ray but from a 

 point midway between the center and the edge of the field. 

 The difference between this ray and half the Field ray, 

 measured on the Y axis, determines the distortion. 



5. The Comatic ray, similar to the Field ray but through 

 the nearest marginal point of the lens system. The difference 

 between this and the Field ray measured on the Y axis or with 

 the Zone ray measured on the X axis determines the coma. 



6. The Astigmatic ray, similar to the Comatic ray, but 

 through the most distant marginal point of the lens system. 



