178 



Nobert's 19th band of lines, 112,688 to the inch, which by 

 the formula subtend an angle of 221 seconds, or above three 

 minutes and a half, and are then counted with great difficulty. 

 The second row represents nearly the P. angidatum, which 

 no one, as I verily believe, can resolve with 174, at half a 

 minute of angular subtense for the beading. 



Visibility depends upon the aperture of the objective, the 

 reduction of aberration, and the direction of the shadows : — 



(1) Aperture. — The aperture of microscopic objectives 

 varies from 170° to 10°, as usually constructed. 



I may here be permitted to state that the first occasion 

 upon which I discovered that the celebrated spikes of the 

 Podura test scale might be resolved into beading, I observed 

 them as black points, whether by solar or artificial light. 

 The cause of this remained unexplained for some years, and I 

 beg here to offer for consideration some experiments which 

 appear satisfactorily to elucidate this singular difficulty. 



Having obtained an apparatus constructed to reduce the 

 aperture of objectives at pleasure, and applied to the " nose " 

 of the instrument before the objective is screwed into its 

 place, it was seen at once that beading of glass, formed of 

 glass threads oOOOth of an inch in diameter, presented 

 different appearances according to the indications of the 

 instrument. 



Thus if the aperture of an excellent objective be reduced 

 one half, the beads assume jet-black borders, so as to present 

 a central light, surrounded by a black ring, and the breadth 

 of the black ring diminishes as the aperture is increased. 

 This affords a clue to the extraordinary dark-brown appear- 

 ance of butterfly scales seen under objectives of small 

 aperture. An assemblage of spherical beading is now pre- 

 sented with black rings, enclosing a light spot, which can 

 only be detected by a surpassing beauty of definition. The 

 objective which presented the black Podura beading was 

 l-6th focal length and aperture 60°, and in other respects a 

 very imperfect combination of glasses. 



(2) If the index of refraction = -, the maximum aperture 



required to define the image formed by a glass spherule is 



83° 38' for parallel rays. The focal length = ^ radius = -?•, 



and the focus is situated at a point distant from the centre 

 _3 



