190 PROCEEDINGS OF THE ACADEMY OF [March, 



alone, different results should be secured according to the character 

 of the object. In the case of structure that could refract but little 

 light the resolution would be cut down to 10 per cent, or less, owing 

 to the large " antipoint, " which would decrease in size and permit of 

 greater resolution as the power of the object to refract rays increased, 

 until in exceptional cases resolution practically equal to that with 

 a full cone should be attainable. On the contrary it will always be 

 found that, without regard to the character of the object, the resolution 

 with central light will be just about one-half that with a full cone, or 

 in other words, will correspond to the diffracted beams admitted by 

 the objective. 



In the absence of suitable rulings, the fact referred to may be demon- 

 strated with diatoms or any other objects that may be at hand in 

 sufficient variety, by noting the finest structure resolved under the two 

 conditions of illumination, and then carefulh r counting the elements 

 of the structure resolved in a given space. On a Moller 60 diatom 

 test plate in styrax, the markings on all its forms having been accu- 

 rately counted and recorded, it was found that the above objective 

 with full cone, resolved Grammatophora serpentina, 48,000 per inch, 

 and with central light reached its limit at the third Navicula lyra, 

 24,800 per inch, confirming the results from the rulings. 



This objective, it may be mentioned, will resolve with oblique light, 

 Navicula Lewisiana, with over 58,000 markings per inch, and thus go 

 considerably beyond the usually accepted theoretical limits for its 

 aperture. The recorded aperture of the objective, measured when 

 purchased many years ago, was .57 N. A., and the markings of the 

 diatom noted as varying from 57,000 per inch near the ends to 59,000 

 at centre of valve. After this resolution was found to be unmistakable, 

 both measurements were repeated. The extreme rays entering the 

 objective were determined by an Abbe apertometer placed on revolving 

 stage with vernier and illuminated by edge of small lamp flame across 

 the room. Two readings to tenth degrees at each "end reaction" 

 agreed exactly, and the results, calculated by taking sine of the half 

 angle multiplied by the refractive index of the apertometer, gave a 

 numerical[aperture of .588 which represents the outside limits. 



A portion of the diatom valve, about half wa}^ between centre and 

 end, which had been noted as being sharply resolved from raphe to 

 margin, was then accurately counted under a high power, and the 

 mean of a number of closely agreeing counts at slightly different 

 points proved to be 58,800 per inch. The number in a full thousandth 

 i nch was counted to avoid the possibility of error in a smaller distance. 



