SUGGESTED IMPROVEMENT IN BINOCULAR MICROSCOPES. 379 



already seen in the beginning of this paper, vary directly with 

 the size of the clear aperture ; but Abbe showed that they also 

 increased in size, as the square of the linear magnification. 

 This is because the distance between the image planes, in which 

 any points of the object which are in planes behind one another 

 come to a true focus, is equal to the square of the distance the 

 points would be apart in the image, supposing they lay in the 

 same plane. For instance, suppose the object were a cube with 

 1-mm. sides, the linear magnification being 10. Then the 

 horizontal sides would appear to be 10 mm., but the distance 

 between the planes in which the top and bottom of the cube 

 were in true focus would be 100 mm.* Suppose, then, we show- 

 both images in the plane in which the top is in focus, it is clear 

 that the diffusion discs from the lower surface will have attained 

 considerable dimensions. 



By means of the accommodation of the eye we can, however, 

 form sharp pictures on the retina of various planes, successively ; 

 and since the size of the diffusion disc varies according to the 

 plane in which they are viewed, we can within certain limits 

 focus our eyes — in other words, change the convexity of the eye- 

 lens — to view that plane in which they are smallest. The extent 

 of this accommodating power varies with the individual, and with 

 his age ; but to give some rough idea, it would enable a normal 

 person to extend the depth perception of the object by about 

 •02 mm., if a wide-angled 1 -in. objective were used with tube-length 

 and ocular to give a magnification of 100 times. But since the 

 solid image of the object increases in depth as the square of the 

 linear magnification, so that the diffusion discs, when referred to 

 any specified plane, vary in size at this same rate, if in the 

 example just given the linear magnification were 1,000, the eye 

 accommodation would only serve to penetrate '0002 mm. ; whilst 



* This presumes the object to be in the air. If imbedded in a medium 

 the distance would be 100 divided by the refractive index of the 

 medium. It is perhaps desirable to here add a word of caution, that it must 

 not be imagined that the exaggerated depth proportions of what we may 

 term the " solid " optical image (usually referred to as the super-magni- 

 fication or super-amplification of the depth dimension) are seen as such. 

 It is not as if we were looking at an ordinary solid object of that shape 

 with unaided vision. What we see, or thiuk we see. depends entirely on the 

 way the optical image affects our eye. and the means at our disposal for 

 perception and judgment— the very matters we are at present considering. 



