DETERMINATION OF THE ANGLE OF APERTURE. 173 



directed towards p do not reach the objective, or are so refracted 

 that they do not reach the eye-piece ; the field of view consequently 

 appears dark. (In the figure this case is indicated by the dotted 

 line x m.) The like result would obtain if a circular dia- 

 phragm D, entirely within the illuminating cone, were brought 

 near to the object p, until its edges touched the bounding surface 

 of the cone. 



The real image is formed between the field-lens and the eye- 

 lens'. From this point the rays again diverge, and are refracted 

 by the eye-lens, so that they appear to come from a point in 

 the optic axis, which is at the distance of distinct vision from 

 the eye. If the eye is adjusted to infinite distance the rays 

 are parallel to each other and to the axis. Conversely, if a pencil 

 of parallel rays is incident on the eye-piece in the direction of 

 the axis, the rays first intersect in p' and then in p, and thence 

 diverge as a solid cone between p a and p b. A screen placed on 

 the left of p at right angles to the axis is therefore illuminated to 

 an extent which is dependent upon the distance from p and the 

 angle of aperture of the objective. If the screen has the form 

 of a circular arc described about p, and is divided into degrees, the 

 angle of aperture may be read off. 



If the source of light a, placed at some distance, isi regarded 

 as the object, its objective-image will appear somewhat behind 

 F' in a. Of this image, the field-lens would form a second one 

 at a" ; but the eye-lens takes up the rays before their union, so 

 that the actual image is now formed at a 1 ". If the light is 

 moved from a to 6, the image passes from a'" to ~b" r ; it disappears, 

 however, as soon as the limiting line b p, or the opposite one a p, 

 is exceeded. The diminution of the image may readily be cal- 

 culated for given distances and focal lengths. If, for instance, the 

 distance of the light from the objective = 1 metre, and the focal 

 lengths of the objective, field-lens, and eye-lens respectively, 5, 50, 

 and 25 mm., and the length of the eye-piece setting 50 mm., we 

 get, with an ordinary tube-length of about 200 mm., a diminution 

 of about 800 linear. 



On the basis of these theoretical deductions sundry practical 

 methods of measuring apertures have been devised, of which we 

 will describe the most simple and efficient. 



(1.) Lister's Method. The Microscope is placed horizontal, and a 

 lamp is adjusted at some distance from the objective in a darkened 



