
PROFESSOR MARTIN DUNCAN’S ADDRESS. 309 

objective—residual uncorrected spherical aberration, in fact ; and 
by others as necessarily inconsistent with perfect definition, even 
with the best methods of construction ; the only approximately 
correct notion regarding it, being that it decreased as the angle of 
aperture increased. 
Professor Abbe, however, in a very valuable paper, placed the 
question on the scientific basis so long needed, showing that the 
total depth of vision in the Microscope, #.e. the solid space which 
at one focus of the Microscope is visible with sufficient distinctness, 
depends not merely on the depth of focus of the objective, but is 
the sum of that and the depth of accommodation by the eye. 
The depth of focus (other conditions remaining the same) varies 
in inverse ratio to the magnifying power and also to the numerical 
aperture of the objective. Thus with a }inch and 2-inch of the 
same aperture the depth of focus of the former would be twice 
that of the latter, or if the powers are the same but the apertures 
are .50 N.A. and 1.50 N.A., it would be as 2 to .66. 
The depth of accommodation depends upon a point which was 
entirely new to microscopists until developed by Professor Abbe, 
viz. the peculiar property of microscopical amplification, by virtue 
of which the linear amplification of the depth of an object is 
largely exaggerated, being equal to the square of the linear ampli- 
fication laterally. Thus an object magnified, according to ordinary 
parlance, roo linear diameters (¢.¢. 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 effect, therefore, of the diminution in the depth of 
focus and depth of accommodation is that the total depth of micros- 
copical 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 accommodation-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 instance, an amplification 
of 30 times is increased to 300, the depth is reduced not to 5 but 
to only ;}; 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. 
