OPTICAL PRINCIPLES OF THE MICROSCOPE. 19 



ously stated at from 5 to 10 inches; but though there arc doubtless 

 many persons whose vision is good at the shorter range, yet the longer 

 is probably the real limit for persons of ordinary vision: who, though 

 they may see an object much nearer the eye, discern little if any more 

 of its details, what is gained in siz-e being lost in distinctness. Now the 

 utility of a convex lens interposed between a near object and the eye, 

 consists in its reducing the divergence of the rays forming the several 

 pencils which issue from it; so that they enter the eye in a state of 

 moderate divergence, as if they had issued from an object beyond the 

 nearest limit of distinct vision, a well-defined picture being thus formed 

 upon the retina. Not only, however, is the course of the several rays 

 in each pencil altered as regards the rest, but the course of the pencils 

 themselves is changed, so that they enter the eye under an angle corre- 

 sponding with that under which they would have arrived from a larger 

 object situated at a greater distance; and thus the picture formed upon 

 the retina by any object (a b, Fig. 12), corresponds in all respects with 

 one which would have been made by the same object increased in its di- 

 mentions to A B, and viewed at the smallest ordinary distance of distinct 

 vision. A ' short-sighted ' person, however, who can only see objects dis- 

 tinctly at a distance of two or three inches, has the same power in his 

 eye alone by reason of its great convexity, as that which the person of 

 ordinary vision gains by the assistance of a convex lens which shall enable 

 him to see at the same distance with equal distinctness. It is evident, 

 therefore, that the magnifying power of a single lens, depending as it 

 does upon the proportion between the distance at which it renders the 

 object visible, and the nearest distance of unaided distinct vision, must 

 be different to different eyes. It is usually estimated, however, by find- 

 ing how many times the focal 

 length of the lens is contained 

 in ten inches; since, in order to 

 render the rays from the object 

 nearly parallel, it must be 

 placed nearly in the focus of 

 the lens (Fig. 3); and the pic- 

 ture is referred by the mind to 

 an object at the ordinary dis- 

 tance. Thus, if the focal 

 length of a lens be one inch, its 

 magnifying power for each di- 

 mension will be 10 times, and 

 consequently 100 superficial; 



While if its focal distance be Dia S m illustrating 'the action of the Simple Micro 



, . . scope ; a b object; A B its magnified image. 



only one-tenth of an inch, its 



magnifying power will be 100 linear, or 10,000 superficial. 



23. But the shorter the focus of the magnifying lens, the smaller 

 must be the diameter of the sphere of which it forms part; and, unless 

 its aperture be proportionately reduced, the distinctness of the image 

 will be destroyed by the spherical and chromatic aberrations ( 9, 12) 

 necessarily resulting from its high curvature. Yet notwithstanding the 

 loss of light and other drawbacks attendant on the use of Single Lenses 

 of high power, they proved of great value to the older Microscopists 

 (among whom Leeuwenhoek should be specially named), on account of 

 their freedom from the errors to which the Compound Microscope of 

 the old construction was necessarily subject; and the amount of excellent 



