S2 THE AMERICAN MONTHLY [March 



A spread slide of P. angulatiim dry on cover is an ex- 

 cellent test. The minimum power required to see it in 

 dots with a J axial cone is about 220 diams. I have my- 

 self glimpsed it with slightly less, but then the image 

 was very difficult. An old cheap student's i N.A. '72 

 showed it with a magnification of 250. Probably some 

 of the modern cheap semi-apochromats would do it with 

 less. The Zeiss apochromatic ? N. A. -65 dots it easily 

 with a large axial cone. It has even been seen with this 

 fine lens with the 8 compensating eyepiece. P. and L. 

 old achromatic 4-10 N.A. -64, power, 290, also does it. 

 All modern students' i and k-, semi-apochromatic or other- 

 wise, should do it also. 



The golden rule for the resolving power of any objec- 

 tive with a i axial cone of illumination is that they should 

 show a fineness of structure equal to 70,000 multiplied by 

 their N.A. Thus— 



Table I. 



Fineness of Structure 



N.A. Resolved. 



01 7,000 



0-2 14,000 



0-3 21,000 



04 28,000 



05 35,000 



0-6 42,000 



0-7 49,000 



0-8 56,000 



0-9 63,000 



1-0 70,000 



1-1 77,000 



1-2 84,000 



1-3 91,000 



1-4 98,000 



1-5 105,000 



Table II. agrees very well with Table I. It must be 

 remembered that some of the lenses which apparently do 

 not come up to the rule gave a very strong resolution of 

 the numbers opposite to them; they therefore would 

 probably have resolved a trifle more, but there was not 

 at hand a slightly finer-marked diatom to test them on. 



