Flat-Warelet Resolution. 589 



of image D (see fig. 11) exceed those o£ image G — is funda- 

 mental in inquiries such as that upon which we are engaged. 

 Now the symbol n in that formula (which is the ratio of the 

 indices of refraction of the media below and above the ob- 

 jective ) is unity in the case of dry objectives, 1*33 for water- 

 immersion objectives, and 1*515 for oil-immersion objectives. 

 The first rule to be observed is as to the use of a scale in 

 making figures to represent the indicator diagram and that 

 part of it which is presented in image x. NA, the numerical 

 aperture of the objective, is n sin u, where n is the n of 

 Lagrange's formula and u is the semi-angular-aperture of the 

 objective, as seen from the point where image C intersects 

 the optic axis. This is a fraction in the case of dry objectives 

 and a number greater than unity in the case of immersion 

 objectives ; and the rule is that we are to adopt such a unit 

 of length for our scale (which we may call the NA scale) as 

 will cause the radius of the visible concentration image to be 

 NA times that unit. It follows from the geometrical pro- 

 perties referred to above, that if we lay off n times the 

 unit of length on the same scale, and employ the length so 

 found as the radius of our reference hemisphere and indicator 

 diagram, then will the concentration image be the central 

 and only visible part of that indicator diagram. 



12. This is illustrated by the accompanying figures which 

 represent the indicator diagram and the concentration image 

 (the image seen at .?.') for four of the objectives and two of 

 the condensers with which the author is accustomed to work, 

 viz. : 



An achromatic of NA = 0'17. 



An apochromatic of NA = 0'65. 



An apochromatic of NA = 0'95. 



An oil-immersion objective of NA=1*35. 



A dry condenser of na = i)' ( d. 



An oil-immersion condenser of na— 1*3. 



Two cases have to be distinguished : 



(a) With dry objectives n—1 ; and as in our figures we are 

 using a two-centimetre scale as our NA scale, the indicator 

 diagram is to have a radius of 2 cm., and the annexed 

 figure- show what portion of it is made visible when, after 

 focussing the microscope upon an object, we remove the 

 eyepiece, insert a blank eyepiece and then look down the 

 tube. An excellent object to employ in making this experi- 

 ment is the diatom Coscinodiscus lineatus, as the details in 

 the concentration image, the visible part of the indicator 



