110 



THE AMERICAN MONTHLY 



[June, 



1 



illuminators of the same refractive 

 index as diamond also. 



Penetrating Power of Objec- 

 tives — Depth of Vision. — This 

 again is a subject which has long 

 been obscure ; very various opinions 

 being held as to the true nature of 

 what has been generally termed the 

 " penetrating power " of an objective. 

 By some it has been declared to be a 

 defect in the construction of the objec- 

 tive — residual, uncorrected, spherical 

 aberration in fact ; and by others as 

 necessarily inconsistent with perfect 

 definition, even with the best methods 

 of construction ; the only approxi- 

 mately 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 mi- 

 croscope is visible with sufficient dis- 

 tinctness, 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 condi- 

 tions 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 ^-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 aper- 

 tures are .50 N. A. and 1.50 N. A., it 

 would be as 2 to .66. 



The depth of accommodation de- 

 pends upon a point which was entirely 

 new to microscopists until developed 

 by Professor Abbe, viz., the peculiar 

 property of microscopical amplifica- 

 tion, by virtue of which the linear 

 amplification of the depth of an ob- 

 ject is largely exaggerated, being 

 equal to the square of the linear 

 amplification laterally. Thus an ob- 

 ject magnified, according to ordinary 

 parlance, 100 linear diameters (/'. e. in 

 breath) 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 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 power we have con- 

 siderable depth of vision, as it is then 

 chiefly influenced by the large accom- 

 modation-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 neces- 

 sarily small also. As the power is 

 further increased, the accommoda- 

 tion-depth ceases to have any influ- 

 ence, 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 tOyV but to only -^ of 

 its original amount ; or, taking the 

 depth of vision with a power of 10 

 times to be 2mm., with powers of 30, 

 100, 300, 1000, and 3000, it is only 

 .254, .0273, .0047, .00094, and .00026 

 mm. 



The formula 



Depth of vision = n \^%^^^fA 



shows at once how much the depth 

 of vision may vary by a change in the 

 conditions — represented by the vari- 

 ous factors in the formula — which 

 make up the total effect, important 

 among which, as will be seen from 

 the form of the equation, is the re- 

 fractive index, n, of the medium in 

 which the object is mounted. 



Micro-stereoscopic Vision. — 

 The determination of the depth of 

 vision (in monocular observation) 



