154 Transactions of the Society. 



amplification laterally. Thus an object magnified, according to 

 ordinary parlance, 100 linear diameters (i. e. in breadth) is 

 magnified 10,000 linear diameters in depth. Now the depth of 

 accommodation varies in inverse ratio to this depth-amplification, 

 that is inversely to the square of the magnifying power, so that 

 whilst large with the low powers, it decreases very rapidly and 

 disproportionately as the power is increased. 



The joint efl'ect, therefore, of the diminution in the depth of 

 focus and depth of accommodation is that the total depth of 

 microscopical vision diminishes, not in the same ratio as the increase 

 in the magnifying power, but at first in a much greater ratio. 

 With the low powers we have considerable depth of vision, as it is 

 then chiefly influenced by the large accomuiodation-depth. As we 

 proceed to the medium powers (100-300) the accommodation-depth 

 very rapidly diminishes, and becomes equal to that of the small 

 depth of focus, so that the total depth of vision is necessarily small 

 also. As the power is further increased, the accommodation-depth 

 ceases to have any influence, and the depth of vision becomes 

 principally depth of focus only. If, for iu stance, an amplification 

 of 30 times is increased to 300, the depth is reduced not to 

 yV but to only Jq of its original amount ; or taking the depth of 

 vision with a power of 10 times to be 2 mm., with powers of 

 30, 100, 300, 1000, and 3000, it is only -254, -0273, '0047, 

 •00094, and •00026 mm. 



The formula 



/L* La)\ 



Depth of vision = '^^N^^"^Naj 



shows at once how much the depth of vision may vary by a change 

 in the conditions — represented by the various factors in the formula 

 — which make up the total efiect, important among which, as will 

 be seen from the form of the equation, is the refractive index n of 

 the medium in which the object is mounted. 



Micro-Stereoscopic Vision. 



The determination of the depth of vision (in monocular ob- 

 servation) naturally throws great light also on the conditions for 

 efiective micro-stereoscopic vision. It is obviously only when an 

 object can be completely seen in all three dimensions at one adjust- 

 ment of the focus, that a true stereoscopic image of it can be 

 obtained. So long as only a single layer of inappreciable depth is 

 visible simultaneously with any distinctness, no stereoscopic appa- 

 ratus, however perfect, can bring into view the form of the whole 

 of the object. 



Now with low powers we have large visual depth, so that objects 

 of considerable thickness can be seen as solids. By reason, however. 



