Hagen.] 168 [November 10, 



distance of the whole microscope (not of the objective) would be 

 equal to - — .5 mill., with a magnifying power of four hundred diam- 

 eters for a visual distance of two hundred mill. 



In the Listing instrument the order of the cardinal points would be 

 inverted and analogous to a convex lens, with a focal distance of the 

 whole microscope equal to -j- .04 mill., with a magnifying power of 

 five thousand diameters. In the first case the objective would have a 

 focal distance of three mill.; in the last of one mill. The difference 

 between the two chief points of the whole microscope is in both cases 

 nearly equal to the whole length of the tube. In the last arrange- 

 ment the whole microscope is analogous to a convex lens with very- 

 short focal distance. 



In a second paper Professor Listing gives further facts concerning 

 this arrangement. An objective with a focal distance of one mill. 

 (=^), has the first image two hundred and one mill, distant from 

 the second chief point. The first magnifying is = 200. The. middle 

 eye-piece of two achromatic lenses with twenty five mill, focal dis- 

 tance, and fifteen mill, distance from each other, gives a focal dis- 

 tance of eighteen mill., and so the second magnifying is = 9. This 

 apparatus, having the objective and middle eye-piece combined with 

 the five eye-pieces of Hartnack (magnifying from three and eight 

 tenths to eleven diameters), gives a total power of from six thousand 

 eight hundred and forty to nineteen thousand eight hundred diame- 

 ters, with a tube of four hundred and forty mill. 



Professor Listing advises that the lenses of the eye-piece should be 

 made of fifteen mill, diameter, and with a correction for their dis- 

 tance. For the middle eye-piece, perhaps, lenses of quartz combined 

 with a lower (1.61 to 1.59) flint glass should be used. In another 

 place he gives a different construction for the middle eye-piece, 

 analogous to an objective of two glasses, but with greater dimensions, 

 and calculates the magnifying power of this to be from twenty two 

 thousand to as much as twenty five thousand six hundred diameters. 



Professor Listing observes that only the penetrating power would 

 be raised by this method of construction, but that to a very conside- 

 rable degree, 



