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XV. — On Ghost Images seen in the Secondaries of Coscinodiscus 

 Aster omphalus, with some Remarks on the Highest Useful 

 Ratio of Magnifying Power to Aperttire. 



By A. A. C. Eliot Merlin. 



(Read October 16, 1907.) 



Most critical workers are probably well acquainted with the 

 beautifully defined ghost images of the substage condenser-stops 

 afforded by the primaries of many diatoms, for those yielded by 

 the perforations of the coarser forms may be well observed under 

 quite moderate powers, the supporting arm, or arms, of the stop 

 being also often sharply pictured. In the old days, distinct 

 dotted resolution of the P. angulat^im was frequently attained in 

 this way with the central stops of Gillett's condenser, under poor 

 objectives hardly capable of plainly rendering the structure with a 

 central cone, what was thus seen being merely the tiny black stop 

 images formed in the perforations, although it is needless to say 

 that the proper demonstration of these images as clean, well- 

 defined disks in such small holes as those in question requires 

 careful manipulation and the best modern lenses. 



Some time ago Mr. E. M. Nelson suggested that it would be 

 interesting to ascertain the smallest perforation in which the con- 

 denser stop-image could be seen with the finest modern objectives 

 and appliances ; and it occurred to me to try the secondaries of 

 Coscinodiscus asteromphalus under a picked Zeiss 3 mm. apochromat 

 of measured N.A. 1'42, employed in conjunction with Powell's dry 

 apochromatic substage condenser. With this arrangement it was 

 found that perfectly well-defined jet black ghost images of the stop 

 were distinguishable as sharp round disks in many of the cap 

 perforations, it being necessary to use a x 40 ocular to attain suffi- 

 cient magnification to exhibit them well, for with a x 12 eye-piece 

 they appeared to be merely tiny black specks. 



In order to measure the exact size of the perforations, the 

 particular specimen of C. asteromphalus was photographed by 

 sunlight from a heliostat, with the secondaries in black dot focus, 

 the sun's image being sharply projected on the object with the full 

 aperture of Powell's dry apochromatic condenser, the 3 mm, 

 ol3Jective and an eye-piece being used so as to obtain a direct 

 magnification of 3400 on the plate. The average diameter of 

 the secondaries thus photographed was found to be • 03 inch ; 

 this, divided by 3400, makes 0-000008826 inch. In order to 



