10 



Transactions of the Society. 



in a cone of an angle of from 140^ to 175° it is nonsense to talk of 

 this question as settled by theory. We shall continue to see closer 

 Hues just in proportion as Microscopes and modes of illumination 

 are improved." * 



That has long been the firm opinion of the writer. In the first 

 paper on the subject of the limits of vision, he stated, " I believe 

 this limit has not yet been reached;"! and farther on, p. 181, 

 " With special adaptations to subdue or destroy the brilliant diffrac- 

 tions of too bright an illumination, many minute details before 

 completely effaced may be brought into distinct revelation." When 

 these remarks were made, the microscopical world had been recently 

 favoured with the beautiful formula introduced independently, I 

 believe, by Professors Helmholtz and Abbe, in which further eluci- 

 dation of the principle was given by a new formula including the 

 semi-angle of aperture of the objective used. Applying these 

 similar results, 1 obtained, for mean rays of wave-length, 4-GT82 of 

 an inch (46,000th nearly) the following results: — 



A Table of Proportionate Eesolving Powers % (some of the details 

 of which were as follows) : — 



Full Aperture 

 of Object-glass. 



179° 

 175° 

 150° 

 120° 



12° 38' 



Troportionate Eesolving Power. 



sill, a = 9999G per inch 

 sill, a = 99905 

 sin. a = 96590 „ 

 sin. a = 86600 „ 

 sill, a = 11000 



Semi-aperture. 



89J° 



m° 



60° 

 G° 19' 



I hope to show in the following paper that however truly this 

 optical law may be deduced from the premisses, it utterly fails for 

 minute dark lines. 



An announcement that it is possible to descry with microscopic 

 apparatus the millionth of an inch would be almost too startling to 

 believe. The human eye can distinguish a hair under favourable 

 conditions of light and background subtending an angle of even 

 less than a second. The black line dividing close double stars, such 

 as Xt Ursae Majoris, which are both of the same (fourth) magnitude, 

 does not subtend in the telescope with a pov?er of 300 diameters 

 many seconds of arc. Besides this, the Microscope differs only from 

 the telescope in the length of its focus and smaller aperture, which, 

 according to received dogma, gives great advantages of vision to the 

 instrument with so great an angular aperture. We cannot doubt, 

 either, from the tales of travellers, that birds of prey possess ex- 

 ceedingly acute vision, by which they can descry small objects at a 



* See 'Month. Mic. Jour.,' Dec. 1869, quoted by Dr. Woodward, 

 t P. 175, 'M. M. Jour.,' Oct. 1876. % P. 181, ibid. 



