Vol. IX] WOODWORTH— OPTICS OF THE MICROSCOPE 183 



to the diagram used to illustrate Sturm's theory. Supporting 

 the lens obliquely in the sunlight and laying a piece of solio 

 paper in the refracted beam thus making a permanent record 

 of the distribution of the light at that plane. Repeating this 

 at different planes will enable one to secure a very complete 

 record of the transformation. A few of such records are 

 shown in the accompanying figure. 



To contrast the generally accepted hypothetical changes 

 with those actually formed in the beam of light we may 

 designate the following phases of the rectangular pencil form- 

 ing the conoid by Roman numerals and of the actual pencil 

 by letters: (Fig. 3). 



I. The initial phase is the shape of the unaberrated image. 

 We have chosen the four-celled grating commonly employed 

 to illustrate this aberration with the intersections of the lines 

 numbered so that the transformations may be readily followed. 



II. The first oblong phase with a much more rapid decrease 

 in the direction of the meridianal plane represented by the 

 numbers 4, 5 and 6. 



III. The meridianal locus at which the points 4, 5 and 6 

 are assumed to coincide. The shape of the pencil at this region 

 is a line at right angles to the meridianal plane. 



IV. The second oblong phase of the same general character 

 as the first oblong phase but with the lines reversed so that 

 the numbers read 6, 5 and 4. 



V. The second orthographic phase in which the pencil has 

 the same proportions as in the initial phase but with the same 

 reversal of numbers seen in the previous phase. 



VI. The third oblong phase where the numbers on the 

 meridianal plane are further apart than those at right angles 

 to this plane. 



VII. The sagittal locus where the light all concentrates on 

 the meridianal plane as a line along this plane which intersects 

 the sagittal plane at a point at which 2, 5 and 8 are supposed 

 to coincide. 



VIII. The fourth oblong phase of the same shape as the 

 third phase but with the position of the points 2, 5 and 8 

 inverted. 



