MEMOlltS ()|- TMK NATIONAI- ACADEMY OK HCIKNCHIH. 47 



cli'iiu'iits of wliii'li tlio liclil is niailc ami wliirli can still Ix- distiti^'iiislicd as sc|tai'a(<' i-li-iin-iils is 



about 4".5 ^_ ,itrt"i is lueasurcd in indies. This is pntvi'd in all works on tin- \viiv«! tlieory of 



light iviul is in arcordance with fX|>erienco. Now this supposition conesiionds precisely with tin- 

 couditions of vision throujih an optically perfect apparatus of tlu^ type under cM»nsideraliou. save 



that the tield is uiaL'uilied in the ratio " for the telescope and n ". ^ iu those systems when 

 o"i rt"i a 



(i is not imleliuitely great, consequently iu such eases the lineness of division of the tield may lie 



increased in these ratios, lleuce the defining i>ower of a telescope may be expressed by 



nd in the otlior class by 



.»rl'" "". .»rl' 



4".5'"', "'"'' =4".r, '^^ 



<(", H<("10'" 10 rt 



The former ..f those equations is a familiar one and need not be further discussed, but the 

 latter contains the whole theory of the deliliiug power of the microscope, and is therefore worthy 

 of a brief consideration. 



From what appears in the discussion of the relation of rt^i to «" we see that the fornu-risthe 

 image of the latter, and also that a°, being a portion of the incident wave surface, is not i)la'>e as 

 is, very nearly, «",. We see, moreover, that the greatest i)ossible diameter of a" is 2rf, in which 

 case the incident wave surface would be hemispherical, whence the maximum possible resolving 

 l)ower of a microscope is 



4".5 _ 

 20 n 



To reduce this to linear value wo have only to multiply by 10'", whence we have, as the 

 closest lines which can be resolved by a microscope 



2".25— =0.'"00001li, 

 7^ n 



in other words.the finest divisions which can be seen with any microscope in which the objective 

 is "dry" are about 100,001) to the inch, which, for a ''homogeneous immersion" objective may rise 

 to 150,000. Since the greatest value known for n in any transparent medium is about 'l.n we 

 may say with certainty that there is no hope of ever making a greater number of lines than a 

 quarter of a million to the inch visible. 



