Microscopical Researches in High Power Definition. 261 



of angular aperture of the objective employed, and directly as the 

 wave-length of the kind of light employed.* 



Professor Helmholtz and Professor Abbe have independently arrived 

 at this beautiful law. And Professor Helmholtz cautiously states, how- 

 ever, there may be some conditions which may modify this law. 



It follows from this principle that thin brilliant lines of light can be 

 best separated by glasses of the highest angular aperture; and the 

 separating power can be measured by the sine of the semi- aperture. 

 Now for wave-length -g-oWot we may thus tabulate them (when -|A,= 

 100,000) :— 



The Values of efor Different Apertures. 



A-perture. («,) the limit of proximity 



of bright lines or disks. 



180 100,000th of an inch. 



160 98,480th 



140 93,970th 



100 76,600th 



60 50,000th 



40 34,200th 



20 17,300th 



15 13,000th 



10 8,700th 



5 4,360th 



1 870th 



i 436th 



Such values as these have accordingly been generally accepted as 

 limits to the resolvability of close lines with objectives of given aper- 

 tures. Further, it is said that lines drawn at the rate of a hundred 

 thousand to the inch represent the limit of microscopic visibility. 



In a paper on this subject by the author it has been shown that a 

 bright space enclosed between two spider-lines, miniatured so as to 

 form a bright interval tswoooi was distinctly visible, whilst the webs 

 actually were about the 6 q 00 and 7 J 00 of an inch in thickness. J 



Under these circumstances, it was interesting to determine whether 



• t =-JU 



2 . sin a 



X = wave-length ; a — semi-angular aperture ; £ the distance between the centres of 

 the disks in contact. 



f Sir John Herschel estimates the waye-lengths as follows, in parts of an inch — ■ 



X Green 47,560th. 



X Intermediate 49,320th. 



X Blue .. .o 51,110th. 



In round numbers, for bright blue illumination, X = 50 ^ 00 . 

 X " Proc. Camb. Phil. Soc," vol. iii, p. 217. 



